ap.cpp

/*************************************************************************
Copyright (c) Sergey Bochkanov (ALGLIB project).

>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#include "stdafx.h"
#include "ap.h"
#include <limits>
#include <locale.h>
using namespace std;

#if defined(AE_CPU)
#if (AE_CPU==AE_INTEL)

#if AE_COMPILER==AE_MSVC
#include <intrin.h>
#endif

#endif
#endif

// disable some irrelevant warnings
#if (AE_COMPILER==AE_MSVC)
#pragma warning(disable:4100)
#pragma warning(disable:4127)
#pragma warning(disable:4702)
#pragma warning(disable:4996)
#endif

/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION IMPLEMENTS BASIC FUNCTIONALITY LIKE
// MEMORY MANAGEMENT FOR VECTORS/MATRICES WHICH IS
// SHARED BETWEEN C++ AND PURE C LIBRARIES
//
/////////////////////////////////////////////////////////////////////////
namespace alglib_impl
{
/*
 * OS-specific includes
 */
#ifdef AE_USE_CPP
}
#endif
#if AE_OS==AE_WINDOWS
#ifndef _WIN32_WINNT
#define _WIN32_WINNT 0x0501
#endif
#include <windows.h>
#include <process.h>
#elif AE_OS==AE_POSIX
#include <time.h>
#include <unistd.h>
#include <pthread.h>
#include <sched.h>
#endif
/* Debugging helpers for Windows */
#ifdef AE_DEBUG4WINDOWS
#include <windows.h>
#include <stdio.h>
#endif
#ifdef AE_USE_CPP
namespace alglib_impl
{
#endif

/*
 * local definitions
 */
#define x_nb 16
#define AE_DATA_ALIGN 64
#define AE_PTR_ALIGN sizeof(void*)
#define DYN_BOTTOM ((void*)1)
#define DYN_FRAME  ((void*)2)
#define AE_LITTLE_ENDIAN 1
#define AE_BIG_ENDIAN 2
#define AE_MIXED_ENDIAN 3
#define AE_SER_ENTRY_LENGTH 11
#define AE_SER_ENTRIES_PER_ROW 5

#define AE_SM_DEFAULT 0
#define AE_SM_ALLOC 1
#define AE_SM_READY2S 2
#define AE_SM_TO_STRING 10
#define AE_SM_FROM_STRING 20
#define AE_SM_TO_CPPSTRING 11

#define AE_LOCK_CYCLES 512
#define AE_LOCK_TESTS_BEFORE_YIELD 16
#define AE_CRITICAL_ASSERT(x) if( !(x) ) abort()

/*************************************************************************
Lock.

This is internal structure which implements lock functionality.
*************************************************************************/
typedef struct
{
#if AE_OS==AE_WINDOWS
    volatile ae_int_t * volatile p_lock;
    char buf[sizeof(ae_int_t)+AE_LOCK_ALIGNMENT];
#elif AE_OS==AE_POSIX
    pthread_mutex_t mutex;
#else
    ae_bool is_locked;
#endif
} _lock;


/*
 * alloc counter
 */
ae_int64_t _alloc_counter = 0;
ae_bool    _use_alloc_counter = ae_false;
#ifdef AE_SMP_DEBUGCOUNTERS
__declspec(align(AE_LOCK_ALIGNMENT)) volatile ae_int64_t _ae_dbg_lock_acquisitions = 0;
__declspec(align(AE_LOCK_ALIGNMENT)) volatile ae_int64_t _ae_dbg_lock_spinwaits = 0;
__declspec(align(AE_LOCK_ALIGNMENT)) volatile ae_int64_t _ae_dbg_lock_yields = 0;
#endif

/*
 * These declarations are used to ensure that
 * sizeof(ae_int32_t)==4, sizeof(ae_int64_t)==8, sizeof(ae_int_t)==sizeof(void*).
 * they will lead to syntax error otherwise (array size will be negative).
 *
 * you can remove them, if you want - they are not used anywhere.
 *
 */
static char _ae_int32_t_must_be_32_bits_wide[1-2*((int)(sizeof(ae_int32_t))-4)*((int)(sizeof(ae_int32_t))-4)];
static char _ae_int64_t_must_be_64_bits_wide[1-2*((int)(sizeof(ae_int64_t))-8)*((int)(sizeof(ae_int64_t))-8)];
static char _ae_int_t_must_be_pointer_sized [1-2*((int)(sizeof(ae_int_t))-(int)sizeof(void*))*((int)(sizeof(ae_int_t))-(int)(sizeof(void*)))];  

/*
 * This variable is used to prevent some tricky optimizations which may degrade multithreaded performance.
 * It is touched once in the ae_init_pool() function from smp.c in order to prevent optimizations.
 *
 */
static volatile ae_int_t ae_never_change_it = 1;

ae_int_t ae_misalignment(const void *ptr, size_t alignment)
{
    union _u
    {
        const void *ptr;
        ae_int_t iptr;
    } u;
    u.ptr = ptr;
    return (ae_int_t)(u.iptr%alignment);
}

void* ae_align(void *ptr, size_t alignment)
{
    char *result = (char*)ptr;
    if( (result-(char*)0)%alignment!=0 )
        result += alignment - (result-(char*)0)%alignment;
    return result;
}

void ae_break(ae_state *state, ae_error_type error_type, const char *msg)
{
#ifndef AE_USE_CPP_ERROR_HANDLING
    if( state!=NULL )
    {
        if( state->thread_exception_handler!=NULL )
            state->thread_exception_handler(state);
        ae_state_clear(state);
        state->last_error = error_type;
        state->error_msg = msg;
        if( state->break_jump!=NULL )
            longjmp(*(state->break_jump), 1);
        else
            abort();
    }
    else
        abort();
#else
    if( state!=NULL )
    {
        if( state->thread_exception_handler!=NULL )
            state->thread_exception_handler(state);
        ae_state_clear(state);
        state->last_error = error_type;
        state->error_msg = msg;
    }
    throw error_type;
#endif
}

void* aligned_malloc(size_t size, size_t alignment)
{
    if( size==0 )
        return NULL;
    if( alignment<=1 )
    {
        /* no alignment, just call malloc */
        void *block;
        void **p; ;
        block = malloc(sizeof(void*)+size);
        if( block==NULL )
            return NULL;
        p = (void**)block;
        *p = block;
        if( _use_alloc_counter )
        {
#if AE_OS==AE_WINDOWS
            InterlockedIncrement((LONG volatile *)&_alloc_counter);
#else
#endif
        }
        return (void*)((char*)block+sizeof(void*));
    }
    else
    {
        /* align */
        void *block;
        char *result;
        block = malloc(alignment-1+sizeof(void*)+size);
        if( block==NULL )
            return NULL;
        result = (char*)block+sizeof(void*);
        /*if( (result-(char*)0)%alignment!=0 )
            result += alignment - (result-(char*)0)%alignment;*/
        result = (char*)ae_align(result, alignment);
        *((void**)(result-sizeof(void*))) = block;
        if( _use_alloc_counter )
        {
#if AE_OS==AE_WINDOWS
            InterlockedIncrement((LONG volatile *)&_alloc_counter);
#else
#endif
        }
        return result;
    }
}

void aligned_free(void *block)
{
    void *p;
    if( block==NULL )
        return;
    p = *((void**)((char*)block-sizeof(void*)));
    free(p);
    if( _use_alloc_counter )
    {
#if AE_OS==AE_WINDOWS
        InterlockedDecrement((LONG volatile *)&_alloc_counter);
#else
#endif
    }
}

/************************************************************************
Malloc's memory with automatic alignment.

Returns NULL when zero size is specified.

Error handling:
* if state is NULL, returns NULL on allocation error
* if state is not NULL, calls ae_break() on allocation error
************************************************************************/
void* ae_malloc(size_t size, ae_state *state)
{
    void *result;
    if( size==0 )
        return NULL;
    result = aligned_malloc(size,AE_DATA_ALIGN);
    if( result==NULL && state!=NULL)
        ae_break(state, ERR_OUT_OF_MEMORY, "ae_malloc(): out of memory");
    return result;
}

void ae_free(void *p)
{
    if( p!=NULL )
        aligned_free(p);
}

/************************************************************************
Sets pointers to the matrix rows.

* dst must be correctly initialized matrix
* dst->data.ptr points to the beginning of memory block  allocated  for  
  row pointers.
* dst->ptr - undefined (initialized during algorithm processing)
* storage parameter points to the beginning of actual storage
************************************************************************/
void ae_matrix_update_row_pointers(ae_matrix *dst, void *storage)
{
    char *p_base;
    void **pp_ptr;
    ae_int_t i;
    if( dst->rows>0 && dst->cols>0 )
    {
        p_base = (char*)storage;
        pp_ptr = (void**)dst->data.ptr;
        dst->ptr.pp_void = pp_ptr;
        for(i=0; i<dst->rows; i++, p_base+=dst->stride*ae_sizeof(dst->datatype))
            pp_ptr[i] = p_base;
    }
    else
        dst->ptr.pp_void = NULL;
}

/************************************************************************
Returns size of datatype.
Zero for dynamic types like strings or multiple precision types.
************************************************************************/
ae_int_t ae_sizeof(ae_datatype datatype)
{
    switch(datatype)
    {
        case DT_BOOL:       return (ae_int_t)sizeof(ae_bool);
        case DT_INT:        return (ae_int_t)sizeof(ae_int_t);
        case DT_REAL:       return (ae_int_t)sizeof(double);
        case DT_COMPLEX:    return 2*(ae_int_t)sizeof(double);
        default:            return 0;
    }
}


/************************************************************************
This  dummy  function  is  used to prevent compiler messages about unused
locals in automatically generated code.

It makes nothing - just accepts pointer, "touches" it - and that is  all.
It performs several tricky operations without side effects which  confuse
compiler so it does not compain about unused locals in THIS function.
************************************************************************/
void ae_touch_ptr(void *p)
{
    void * volatile fake_variable0 = p;
    void * volatile fake_variable1 = fake_variable0;
    fake_variable0 = fake_variable1;
}

/************************************************************************
This function initializes ALGLIB environment state.

NOTES:
* stacks contain no frames, so ae_make_frame() must be called before
  attaching dynamic blocks. Without it ae_leave_frame() will cycle
  forever (which is intended behavior).
************************************************************************/
void ae_state_init(ae_state *state)
{
    ae_int32_t *vp;

    /*
     * p_next points to itself because:
     * * correct program should be able to detect end of the list
     *   by looking at the ptr field.
     * * NULL p_next may be used to distinguish automatic blocks
     *   (in the list) from non-automatic (not in the list)
     */
    state->last_block.p_next = &(state->last_block);
    state->last_block.deallocator = NULL;
    state->last_block.ptr = DYN_BOTTOM;
    state->p_top_block = &(state->last_block);
#ifndef AE_USE_CPP_ERROR_HANDLING
    state->break_jump = NULL;
#endif
    state->error_msg = "";
    
    /*
     * determine endianness and initialize precomputed IEEE special quantities.
     */
    state->endianness = ae_get_endianness();
    if( state->endianness==AE_LITTLE_ENDIAN )
    {
        vp = (ae_int32_t*)(&state->v_nan);
        vp[0] = 0;
        vp[1] = (ae_int32_t)0x7FF80000;
        vp = (ae_int32_t*)(&state->v_posinf);
        vp[0] = 0;
        vp[1] = (ae_int32_t)0x7FF00000;
        vp = (ae_int32_t*)(&state->v_neginf);
        vp[0] = 0;
        vp[1] = (ae_int32_t)0xFFF00000;
    }
    else if( state->endianness==AE_BIG_ENDIAN )
    {
        vp = (ae_int32_t*)(&state->v_nan);
        vp[1] = 0;
        vp[0] = (ae_int32_t)0x7FF80000;
        vp = (ae_int32_t*)(&state->v_posinf);
        vp[1] = 0;
        vp[0] = (ae_int32_t)0x7FF00000;
        vp = (ae_int32_t*)(&state->v_neginf);
        vp[1] = 0;
        vp[0] = (ae_int32_t)0xFFF00000;
    }
    else
        abort();
    
    /*
     * set threading information
     */
    state->worker_thread = NULL;
    state->parent_task = NULL;
    state->thread_exception_handler = NULL;
}


/************************************************************************
This function clears ALGLIB environment state.
All dynamic data controlled by state are freed.
************************************************************************/
void ae_state_clear(ae_state *state)
{
    while( state->p_top_block->ptr!=DYN_BOTTOM )
        ae_frame_leave(state);
}


#ifndef AE_USE_CPP_ERROR_HANDLING
/************************************************************************
This function sets jump buffer for error handling.

buf may be NULL.
************************************************************************/
void ae_state_set_break_jump(ae_state *state, jmp_buf *buf)
{
    state->break_jump = buf;
}
#endif


/************************************************************************
This function makes new stack frame.

This function takes two parameters: environment state and pointer to  the
dynamic block which will be used as indicator  of  the  frame  beginning.
This dynamic block must be initialized by caller and mustn't  be changed/
deallocated/reused till ae_leave_frame called. It may be global or  local
variable (local is even better).
************************************************************************/
void ae_frame_make(ae_state *state, ae_frame *tmp)
{
    tmp->db_marker.p_next = state->p_top_block;
    tmp->db_marker.deallocator = NULL;
    tmp->db_marker.ptr = DYN_FRAME;
    state->p_top_block = &tmp->db_marker;
}


/************************************************************************
This function leaves current stack frame and deallocates all automatic
dynamic blocks which were attached to this frame.
************************************************************************/
void ae_frame_leave(ae_state *state)
{
    while( state->p_top_block->ptr!=DYN_FRAME && state->p_top_block->ptr!=DYN_BOTTOM)
    {
        if( state->p_top_block->ptr!=NULL && state->p_top_block->deallocator!=NULL)
            ((ae_deallocator)(state->p_top_block->deallocator))(state->p_top_block->ptr);
        state->p_top_block = state->p_top_block->p_next;
    }
    state->p_top_block = state->p_top_block->p_next;
}


/************************************************************************
This function attaches block to the dynamic block list

block               block
state               ALGLIB environment state

NOTES:
* never call it for special blocks which marks frame boundaries!
************************************************************************/
void ae_db_attach(ae_dyn_block *block, ae_state *state)
{
    block->p_next = state->p_top_block;
    state->p_top_block = block;
}


/************************************************************************
This function malloc's dynamic block:

block               destination block, assumed to be uninitialized
size                size (in bytes)
state               ALGLIB environment state. May be NULL.
make_automatic      if true, vector is added to the dynamic block list

block is assumed to be uninitialized, its fields are ignored.

Error handling:
* if state is NULL, returns ae_false on allocation error
* if state is not NULL, calls ae_break() on allocation error
* returns ae_true on success

NOTES:
* never call it for blocks which are already in the list
************************************************************************/
ae_bool ae_db_malloc(ae_dyn_block *block, ae_int_t size, ae_state *state, ae_bool make_automatic)
{
    /* ensure that size is >=0
       two ways to exit: 1) through ae_assert, if we have non-NULL state, 2) by returning ae_false */
    if( state!=NULL )
        ae_assert(size>=0, "ae_db_malloc(): negative size", state);
    if( size<0 )
        return ae_false;
    
    /* allocation */
    block->ptr = ae_malloc((size_t)size, state);
    if( block->ptr==NULL && size!=0 )
    {
        /* for state!=NULL exception is thrown from ae_malloc(), so
           we have to handle only situation when state is NULL */
        return ae_false;
    }
    if( make_automatic && state!=NULL )
        ae_db_attach(block, state);
    else
        block->p_next = NULL;
    block->deallocator = ae_free;
    return ae_true;
}


/************************************************************************
This function realloc's dynamic block:

block               destination block (initialized)
size                new size (in bytes)
state               ALGLIB environment state

block is assumed to be initialized.

This function:
* deletes old contents
* preserves automatic state

Error handling:
* if state is NULL, returns ae_false on allocation error
* if state is not NULL, calls ae_break() on allocation error
* returns ae_true on success

NOTES:
* never call it for special blocks which mark frame boundaries!
************************************************************************/
ae_bool ae_db_realloc(ae_dyn_block *block, ae_int_t size, ae_state *state)
{
    /* ensure that size is >=0
       two ways to exit: 1) through ae_assert, if we have non-NULL state, 2) by returning ae_false */
    if( state!=NULL )
        ae_assert(size>=0, "ae_db_realloc(): negative size", state);
    if( size<0 )
        return ae_false;
    
    /* realloc */
    if( block->ptr!=NULL )
        ((ae_deallocator)block->deallocator)(block->ptr);
    block->ptr = ae_malloc((size_t)size, state);
    if( block->ptr==NULL && size!=0 )
    {
        /* for state!=NULL exception is thrown from ae_malloc(), so
           we have to handle only situation when state is NULL */
        return ae_false;
    }
    block->deallocator = ae_free;
    return ae_true;
}


/************************************************************************
This function clears dynamic block (releases  all  dynamically  allocated
memory). Dynamic block may be in automatic management list - in this case
it will NOT be removed from list.

block               destination block (initialized)

NOTES:
* never call it for special blocks which marks frame boundaries!
************************************************************************/
void ae_db_free(ae_dyn_block *block)
{
    if( block->ptr!=NULL )
        ((ae_deallocator)block->deallocator)(block->ptr);
    block->ptr = NULL;
    block->deallocator = ae_free;
}

/************************************************************************
This function swaps contents of two dynamic blocks (pointers and 
deallocators) leaving other parameters (automatic management settings, 
etc.) unchanged.

NOTES:
* never call it for special blocks which marks frame boundaries!
************************************************************************/
void ae_db_swap(ae_dyn_block *block1, ae_dyn_block *block2)
{
    void (*deallocator)(void*) = NULL;
    void * volatile ptr;
    ptr = block1->ptr;
    deallocator = block1->deallocator;
    block1->ptr = block2->ptr;
    block1->deallocator = block2->deallocator;
    block2->ptr = ptr;
    block2->deallocator = deallocator;
}

/************************************************************************
This function creates ae_vector.

Vector size may be zero. Vector contents is uninitialized.

dst                 destination vector
size                vector size, may be zero
datatype            guess what...
state               ALGLIB environment state
make_automatic      if true, vector is added to the dynamic block list

Error handling:
* if state is NULL, returns ae_false on allocation error
* if state is not NULL, calls ae_break() on allocation error
* returns ae_true on success

dst is assumed to be uninitialized, its fields are ignored.
************************************************************************/
ae_bool ae_vector_init(ae_vector *dst, ae_int_t size, ae_datatype datatype, ae_state *state, ae_bool make_automatic)
{
    /* ensure that size is >=0
       two ways to exit: 1) through ae_assert, if we have non-NULL state, 2) by returning ae_false */
    if( state!=NULL )
        ae_assert(size>=0, "ae_vector_init(): negative size", state);
    if( size<0 )
        return ae_false;

    /* init */
    dst->cnt = size;
    dst->datatype = datatype;
    if( !ae_db_malloc(&dst->data, size*ae_sizeof(datatype), state, make_automatic) )
        return ae_false;
    dst->ptr.p_ptr = dst->data.ptr;
    return ae_true;
}


/************************************************************************
This function creates copy of ae_vector.

dst                 destination vector
src                 well, it is source
state               ALGLIB environment state
make_automatic      if true, vector is added to the dynamic block list

Error handling:
* if state is NULL, returns ae_false on allocation error
* if state is not NULL, calls ae_break() on allocation error
* returns ae_true on success

dst is assumed to be uninitialized, its fields are ignored.
************************************************************************/
ae_bool ae_vector_init_copy(ae_vector *dst, ae_vector *src, ae_state *state, ae_bool make_automatic)
{
    if( !ae_vector_init(dst, src->cnt, src->datatype, state, make_automatic) )
        return ae_false;
    if( src->cnt!=0 )
        memcpy(dst->ptr.p_ptr, src->ptr.p_ptr, (size_t)(src->cnt*ae_sizeof(src->datatype)));
    return ae_true;
}

/************************************************************************
This function initializes ae_vector using X-structure as source. New copy
of data is created, which is owned/managed by ae_vector  structure.  Both
structures (source and destination) remain completely  independent  after
this call.

dst                 destination matrix
src                 well, it is source
state               ALGLIB environment state
make_automatic      if true, matrix is added to the dynamic block list

Error handling:
* calls ae_break() on allocation error

dst is assumed to be uninitialized, its fields are ignored.
************************************************************************/
void ae_vector_init_from_x(ae_vector *dst, x_vector *src, ae_state *state, ae_bool make_automatic)
{
    ae_vector_init(dst, (ae_int_t)src->cnt, (ae_datatype)src->datatype, state, make_automatic);
    if( src->cnt>0 )
        memcpy(dst->ptr.p_ptr, src->ptr, (size_t)(((ae_int_t)src->cnt)*ae_sizeof((ae_datatype)src->datatype)));
}

/************************************************************************
This function initializes ae_vector using X-structure as source.

New vector is attached to source:
* DST shares memory with SRC
* both DST and SRC are writable - all writes to DST  change  elements  of
  SRC and vice versa.
* DST can be reallocated with ae_vector_set_length(), in  this  case  SRC
  remains untouched
* SRC, however, CAN NOT BE REALLOCATED AS LONG AS DST EXISTS

dst                 destination vector
src                 well, it is source
state               ALGLIB environment state
make_automatic      if true, vector is added to the dynamic block list

Error handling:
* calls ae_break() on allocation error

dst is assumed to be uninitialized, its fields are ignored.
************************************************************************/
void ae_vector_attach_to_x(ae_vector *dst, x_vector *src, ae_state *state, ae_bool make_automatic)
{
    ae_int_t cnt;
    
    cnt = (ae_int_t)src->cnt;
    
    /* ensure that size is correct */
    ae_assert(cnt==src->cnt,  "ae_vector_attach_to_x(): 32/64 overflow", state);
    ae_assert(cnt>=0,         "ae_vector_attach_to_x(): negative length", state);
    
    /* init */
    dst->cnt = cnt;
    dst->datatype = (ae_datatype)src->datatype;
    dst->ptr.p_ptr = src->ptr;
    ae_assert(
        ae_db_malloc(&dst->data, 0, state, make_automatic),
        "ae_vector_attach_to_x(): malloc error",
        state);
}

/************************************************************************
This function changes length of ae_vector.

dst                 destination vector
newsize             vector size, may be zero
state               ALGLIB environment state

Error handling:
* if state is NULL, returns ae_false on allocation error
* if state is not NULL, calls ae_break() on allocation error
* returns ae_true on success

NOTES:
* vector must be initialized
* all contents is destroyed during setlength() call
* new size may be zero.
************************************************************************/
ae_bool ae_vector_set_length(ae_vector *dst, ae_int_t newsize, ae_state *state)
{
    /* ensure that size is >=0
       two ways to exit: 1) through ae_assert, if we have non-NULL state, 2) by returning ae_false */
    if( state!=NULL )
        ae_assert(newsize>=0, "ae_vector_set_length(): negative size", state);
    if( newsize<0 )
        return ae_false;

    /* set length */
    if( dst->cnt==newsize )
        return ae_true;
    dst->cnt = newsize;
    if( !ae_db_realloc(&dst->data, newsize*ae_sizeof(dst->datatype), state) )
        return ae_false;
    dst->ptr.p_ptr = dst->data.ptr;
    return ae_true;
}


/************************************************************************
This  function  provides  "CLEAR"  functionality  for vector (contents is
cleared, but structure still left in valid state).

The  function clears vector contents (releases all dynamically  allocated
memory). Vector may be in automatic management list  -  in this  case  it
will NOT be removed from list.

IMPORTANT: this function does NOT invalidates dst; it just  releases  all
dynamically allocated storage, but dst still may be used  after  call  to
ae_vector_set_length().

dst                 destination vector
************************************************************************/
void ae_vector_clear(ae_vector *dst)
{
    dst->cnt = 0;
    ae_db_free(&dst->data);
    dst->ptr.p_ptr = 0;
}


/************************************************************************
This  function  provides "DESTROY"  functionality for vector (contents is
cleared, all internal structures are destroyed). For vectors it  is  same
as CLEAR.

dst                 destination vector
************************************************************************/
void ae_vector_destroy(ae_vector *dst)
{
    ae_vector_clear(dst);
}


/************************************************************************
This function efficiently swaps contents of two vectors, leaving other
pararemeters (automatic management, etc.) unchanged.
************************************************************************/
void ae_swap_vectors(ae_vector *vec1, ae_vector *vec2)
{
    ae_int_t cnt;
    ae_datatype datatype;
    void *p_ptr;
    
    ae_db_swap(&vec1->data, &vec2->data);
    
    cnt = vec1->cnt;
    datatype = vec1->datatype;
    p_ptr = vec1->ptr.p_ptr;
    vec1->cnt = vec2->cnt;
    vec1->datatype = vec2->datatype;
    vec1->ptr.p_ptr = vec2->ptr.p_ptr;
    vec2->cnt = cnt;
    vec2->datatype = datatype;
    vec2->ptr.p_ptr = p_ptr;
}

/************************************************************************
This function creates ae_matrix.

Matrix size may be zero, in such cases both rows and cols are zero.
Matrix contents is uninitialized.

dst                 destination natrix
rows                rows count
cols                cols count
datatype            element type
state               ALGLIB environment state
make_automatic      if true, matrix is added to the dynamic block list

Error handling:
* if state is NULL, returns ae_false on allocation error
* if state is not NULL, calls ae_break() on allocation error
* returns ae_true on success

dst is assumed to be uninitialized, its fields are ignored.
************************************************************************/
ae_bool ae_matrix_init(ae_matrix *dst, ae_int_t rows, ae_int_t cols, ae_datatype datatype, ae_state *state, ae_bool make_automatic)
{
    /* ensure that size is >=0
       two ways to exit: 1) through ae_assert, if we have non-NULL state, 2) by returning ae_false */
    if( state!=NULL )
        ae_assert(rows>=0 && cols>=0, "ae_matrix_init(): negative length", state);
    if( rows<0 || cols<0 )
        return ae_false;

    /* if one of rows/cols is zero, another MUST be too */
    if( rows==0 || cols==0 )
    {
        rows = 0;
        cols = 0;
    }

    /* init */
    dst->rows = rows;
    dst->cols = cols;
    dst->stride = cols;
    while( dst->stride*ae_sizeof(datatype)%AE_DATA_ALIGN!=0 )
        dst->stride++;
    dst->datatype = datatype;
    if( !ae_db_malloc(&dst->data, dst->rows*((ae_int_t)sizeof(void*)+dst->stride*ae_sizeof(datatype))+AE_DATA_ALIGN-1, state, make_automatic) )
        return ae_false;
    ae_matrix_update_row_pointers(dst, ae_align((char*)dst->data.ptr+dst->rows*sizeof(void*),AE_DATA_ALIGN));
    return ae_true;
}


/************************************************************************
This function creates copy of ae_matrix.

dst                 destination matrix
src                 well, it is source
state               ALGLIB environment state
make_automatic      if true, matrix is added to the dynamic block list

Error handling:
* if state is NULL, returns ae_false on allocation error
* if state is not NULL, calls ae_break() on allocation error
* returns ae_true on success

dst is assumed to be uninitialized, its fields are ignored.
************************************************************************/
ae_bool ae_matrix_init_copy(ae_matrix *dst, ae_matrix *src, ae_state *state, ae_bool make_automatic)
{
    ae_int_t i;
    if( !ae_matrix_init(dst, src->rows, src->cols, src->datatype, state, make_automatic) )
        return ae_false;
    if( src->rows!=0 && src->cols!=0 )
    {
        if( dst->stride==src->stride )
            memcpy(dst->ptr.pp_void[0], src->ptr.pp_void[0], (size_t)(src->rows*src->stride*ae_sizeof(src->datatype)));
        else
            for(i=0; i<dst->rows; i++)
                memcpy(dst->ptr.pp_void[i], src->ptr.pp_void[i], (size_t)(dst->cols*ae_sizeof(dst->datatype)));
    }
    return ae_true;
}


/************************************************************************
This function initializes ae_matrix using X-structure as source. New copy
of data is created, which is owned/managed by ae_matrix  structure.  Both
structures (source and destination) remain completely  independent  after
this call.

dst                 destination matrix
src                 well, it is source
state               ALGLIB environment state
make_automatic      if true, matrix is added to the dynamic block list

Error handling:
* calls ae_break() on allocation error

dst is assumed to be uninitialized, its fields are ignored.
************************************************************************/
void ae_matrix_init_from_x(ae_matrix *dst, x_matrix *src, ae_state *state, ae_bool make_automatic)
{
    char *p_src_row;
    char *p_dst_row;
    ae_int_t row_size;
    ae_int_t i;
    ae_matrix_init(dst, (ae_int_t)src->rows, (ae_int_t)src->cols, (ae_datatype)src->datatype, state, make_automatic);
    if( src->rows!=0 && src->cols!=0 )
    {
        p_src_row = (char*)src->ptr;
        p_dst_row = (char*)(dst->ptr.pp_void[0]);
        row_size = ae_sizeof((ae_datatype)src->datatype)*(ae_int_t)src->cols;
        for(i=0; i<src->rows; i++, p_src_row+=src->stride*ae_sizeof((ae_datatype)src->datatype), p_dst_row+=dst->stride*ae_sizeof((ae_datatype)src->datatype))
            memcpy(p_dst_row, p_src_row, (size_t)(row_size));
    }
}


/************************************************************************
This function initializes ae_matrix using X-structure as source.

New matrix is attached to source:
* DST shares memory with SRC
* both DST and SRC are writable - all writes to DST  change  elements  of
  SRC and vice versa.
* DST can be reallocated with ae_matrix_set_length(), in  this  case  SRC
  remains untouched
* SRC, however, CAN NOT BE REALLOCATED AS LONG AS DST EXISTS

dst                 destination matrix
src                 well, it is source
state               ALGLIB environment state
make_automatic      if true, matrix is added to the dynamic block list

Error handling:
* calls ae_break() on allocation error

dst is assumed to be uninitialized, its fields are ignored.
************************************************************************/
void ae_matrix_attach_to_x(ae_matrix *dst, x_matrix *src, ae_state *state, ae_bool make_automatic)
{
    ae_int_t rows, cols;
    
    rows = (ae_int_t)src->rows;
    cols = (ae_int_t)src->cols;
    
    /* ensure that size is correct */
    ae_assert(rows==src->rows,      "ae_matrix_attach_to_x(): 32/64 overflow", state);
    ae_assert(cols==src->cols,      "ae_matrix_attach_to_x(): 32/64 overflow", state);
    ae_assert(rows>=0 && cols>=0,   "ae_matrix_attach_to_x(): negative length", state);
    
    /* if one of rows/cols is zero, another MUST be too */
    if( rows==0 || cols==0 )
    {
        rows = 0;
        cols = 0;
    }

    /* init */
    dst->rows = rows;
    dst->cols = cols;
    dst->stride = cols;
    dst->datatype = (ae_datatype)src->datatype;
    dst->ptr.pp_void = NULL;
    ae_assert(
        ae_db_malloc(&dst->data, dst->rows*(ae_int_t)sizeof(void*), state, make_automatic),
        "ae_matrix_attach_to_x(): malloc error",
        state);
    if( dst->rows>0 && dst->cols>0 )
    {
        ae_int_t i, rowsize;
        char *p_row;
        void **pp_ptr;
        
        p_row = (char*)src->ptr;
        rowsize = dst->stride*ae_sizeof(dst->datatype);
        pp_ptr  = (void**)dst->data.ptr;
        dst->ptr.pp_void = pp_ptr;
        for(i=0; i<dst->rows; i++, p_row+=rowsize)
            pp_ptr[i] = p_row;
    }
}


/************************************************************************
This function changes length of ae_matrix.

dst                 destination matrix
rows                size, may be zero
cols                size, may be zero
state               ALGLIB environment state

Error handling:
* if state is NULL, returns ae_false on allocation error
* if state is not NULL, calls ae_break() on allocation error
* returns ae_true on success

NOTES:
* matrix must be initialized
* all contents is destroyed during setlength() call
* new size may be zero.
************************************************************************/
ae_bool ae_matrix_set_length(ae_matrix *dst, ae_int_t rows, ae_int_t cols, ae_state *state)
{
    /* ensure that size is >=0
       two ways to exit: 1) through ae_assert, if we have non-NULL state, 2) by returning ae_false */
    if( state!=NULL )
        ae_assert(rows>=0 && cols>=0, "ae_matrix_set_length(): negative length", state);
    if( rows<0 || cols<0 )
        return ae_false;

    if( dst->rows==rows && dst->cols==cols )
        return ae_true;    
    dst->rows = rows;
    dst->cols = cols;
    dst->stride = cols;
    while( dst->stride*ae_sizeof(dst->datatype)%AE_DATA_ALIGN!=0 )
        dst->stride++;
    if( !ae_db_realloc(&dst->data, dst->rows*((ae_int_t)sizeof(void*)+dst->stride*ae_sizeof(dst->datatype))+AE_DATA_ALIGN-1, state) )
        return ae_false;
    ae_matrix_update_row_pointers(dst, ae_align((char*)dst->data.ptr+dst->rows*sizeof(void*),AE_DATA_ALIGN));
    return ae_true;
}


/************************************************************************
This  function  provides  "CLEAR"  functionality  for vector (contents is
cleared, but structure still left in valid state).

The  function clears matrix contents (releases all dynamically  allocated
memory). Matrix may be in automatic management list  -  in this  case  it
will NOT be removed from list.

IMPORTANT: this function does NOT invalidates dst; it just  releases  all
dynamically allocated storage, but dst still may be used  after  call  to
ae_matrix_set_length().

dst                 destination matrix
************************************************************************/
void ae_matrix_clear(ae_matrix *dst)
{
    dst->rows = 0;
    dst->cols = 0;
    dst->stride = 0;
    ae_db_free(&dst->data);
    dst->ptr.p_ptr = 0;
}


/************************************************************************
This  function  provides  "DESTROY" functionality for matrix (contents is
cleared, but structure still left in valid state).

For matrices it is same as CLEAR.

dst                 destination matrix
************************************************************************/
void ae_matrix_destroy(ae_matrix *dst)
{
    ae_matrix_clear(dst);
}


/************************************************************************
This function efficiently swaps contents of two vectors, leaving other
pararemeters (automatic management, etc.) unchanged.
************************************************************************/
void ae_swap_matrices(ae_matrix *mat1, ae_matrix *mat2)
{
    ae_int_t rows;
    ae_int_t cols;
    ae_int_t stride;
    ae_datatype datatype;
    void *p_ptr;
    
    ae_db_swap(&mat1->data, &mat2->data);
    
    rows = mat1->rows;
    cols = mat1->cols;
    stride = mat1->stride;
    datatype = mat1->datatype;
    p_ptr = mat1->ptr.p_ptr;

    mat1->rows = mat2->rows;
    mat1->cols = mat2->cols;
    mat1->stride = mat2->stride;
    mat1->datatype = mat2->datatype;
    mat1->ptr.p_ptr = mat2->ptr.p_ptr;

    mat2->rows = rows;
    mat2->cols = cols;
    mat2->stride = stride;
    mat2->datatype = datatype;
    mat2->ptr.p_ptr = p_ptr;
}


/************************************************************************
This function creates smart pointer structure.

dst                 destination smart pointer.
                    already allocated, but not initialized.
subscriber          pointer to pointer which receives updates in the
                    internal object stored in ae_smart_ptr. Any update to
                    dst->ptr is translated to subscriber. Can be NULL.
state               ALGLIB environment state
make_automatic      if true, smart pointer is added to the dynamic block list

After initialization, smart pointer stores NULL pointer.

Error handling:
* if state is NULL, returns ae_false on allocation error
* if state is not NULL, calls ae_break() on allocation error
* returns ae_true on success
************************************************************************/
ae_bool ae_smart_ptr_init(ae_smart_ptr *dst, void **subscriber, ae_state *state, ae_bool make_automatic)
{
    dst->subscriber = subscriber;
    dst->ptr = NULL;
    if( dst->subscriber!=NULL )
        *(dst->subscriber) = dst->ptr;
    dst->is_owner = ae_false;
    dst->is_dynamic = ae_false;
    dst->frame_entry.deallocator = ae_smart_ptr_destroy;
    dst->frame_entry.ptr = dst;
    if( make_automatic && state!=NULL )
        ae_db_attach(&dst->frame_entry, state);
    return ae_true;
}


/************************************************************************
This function clears smart pointer structure.

dst                 destination smart pointer.

After call to this function smart pointer contains NULL reference,  which
is  propagated  to  its  subscriber  (in  cases  non-NULL  subscruber was
specified during pointer creation).
************************************************************************/
void ae_smart_ptr_clear(void *_dst)
{
    ae_smart_ptr *dst = (ae_smart_ptr*)_dst;
    if( dst->is_owner && dst->ptr!=NULL )
    {
        dst->destroy(dst->ptr);
        if( dst->is_dynamic )
            ae_free(dst->ptr);
    }
    dst->is_owner = ae_false;
    dst->is_dynamic = ae_false;
    dst->ptr = NULL;
    dst->destroy = NULL;
    if( dst->subscriber!=NULL )
        *(dst->subscriber) = NULL;
}


/************************************************************************
This function dstroys smart pointer structure (same as clearing it).

dst                 destination smart pointer.
************************************************************************/
void ae_smart_ptr_destroy(void *_dst)
{
    ae_smart_ptr_clear(_dst);
}


/************************************************************************
This function assigns pointer to ae_smart_ptr structure.

dst                 destination smart pointer.
new_ptr             new pointer to assign
is_owner            whether smart pointer owns new_ptr
is_dynamic          whether object is dynamic - clearing such object
                    requires BOTH calling destructor function AND calling
                    ae_free() for memory occupied by object.
destroy             destructor function

In case smart pointer already contains non-NULL value and owns this value,
it is freed before assigning new pointer.

Changes in pointer are propagated to its  subscriber  (in  case  non-NULL
subscriber was specified during pointer creation).

You can specify NULL new_ptr, in which case is_owner/destroy are ignored.
************************************************************************/
void ae_smart_ptr_assign(ae_smart_ptr *dst, void *new_ptr, ae_bool is_owner, ae_bool is_dynamic, void (*destroy)(void*))
{
    if( dst->is_owner && dst->ptr!=NULL )
        dst->destroy(dst->ptr);
    if( new_ptr!=NULL )
    {
        dst->ptr = new_ptr;
        dst->is_owner = is_owner;
        dst->is_dynamic = is_dynamic;
        dst->destroy = destroy;
    }
    else
    {
        dst->ptr = NULL;
        dst->is_owner = ae_false;
        dst->is_dynamic = ae_false;
        dst->destroy = NULL;
    }
    if( dst->subscriber!=NULL )
        *(dst->subscriber) = dst->ptr;
}


/************************************************************************
This function releases pointer owned by ae_smart_ptr structure:
* all internal fields are set to NULL
* destructor function for internal pointer is NOT called even when we own
  this pointer. After this call ae_smart_ptr releases  ownership  of  its
  pointer and passes it to caller.
* changes in pointer are propagated to its subscriber (in  case  non-NULL
  subscriber was specified during pointer creation).

dst                 destination smart pointer.
************************************************************************/
void ae_smart_ptr_release(ae_smart_ptr *dst)
{
    dst->is_owner = ae_false;
    dst->is_dynamic = ae_false;
    dst->ptr = NULL;
    dst->destroy = NULL;
    if( dst->subscriber!=NULL )
        *(dst->subscriber) = NULL;
}

/************************************************************************
This function copies contents of ae_vector (SRC) to x_vector (DST).

This function should not be called for  DST  which  is  attached  to  SRC
(opposite situation, when SRC is attached to DST, is possible).

Depending on situation, following actions are performed 
* for SRC attached to DST, this function performs no actions (no need  to
  do anything)
* for independent vectors of different sizes it allocates storage in  DST
  and copy contents of SRC  to  DST.  DST->last_action field  is  set  to
  ACT_NEW_LOCATION, and DST->owner is set to OWN_AE.
* for  independent  vectors   of  same  sizes  it does not perform memory
  (re)allocation.  It  just  copies  SRC  to  already   existing   place.
  DST->last_action   is   set   to    ACT_SAME_LOCATION  (unless  it  was
  ACT_NEW_LOCATION), DST->owner is unmodified.

dst                 destination vector
src                 source, vector in x-format
state               ALGLIB environment state

NOTES:
* dst is assumed to be initialized. Its contents is freed before  copying
  data  from src  (if  size / type  are  different)  or  overwritten  (if
  possible given destination size).
************************************************************************/
void ae_x_set_vector(x_vector *dst, ae_vector *src, ae_state *state)
{
    if( src->ptr.p_ptr == dst->ptr )
    {
        /* src->ptr points to the beginning of dst, attached matrices, no need to copy */
        return;
    }
    if( dst->cnt!=src->cnt || dst->datatype!=src->datatype )
    {
        if( dst->owner==OWN_AE )
            ae_free(dst->ptr);
        dst->ptr = ae_malloc((size_t)(src->cnt*ae_sizeof(src->datatype)), state);
        if( src->cnt!=0 && dst->ptr==NULL )
            ae_break(state, ERR_OUT_OF_MEMORY, "ae_malloc(): out of memory");
        dst->last_action = ACT_NEW_LOCATION;
        dst->cnt = src->cnt;
        dst->datatype = src->datatype;
        dst->owner = OWN_AE;
    }
    else
    {
        if( dst->last_action==ACT_UNCHANGED )
            dst->last_action = ACT_SAME_LOCATION;
        else if( dst->last_action==ACT_SAME_LOCATION )
            dst->last_action = ACT_SAME_LOCATION;
        else if( dst->last_action==ACT_NEW_LOCATION )
            dst->last_action = ACT_NEW_LOCATION;
        else
            ae_assert(ae_false, "ALGLIB: internal error in ae_x_set_vector()", state);
    }
    if( src->cnt )
        memcpy(dst->ptr, src->ptr.p_ptr, (size_t)(src->cnt*ae_sizeof(src->datatype)));
}

/************************************************************************
This function copies contents of ae_matrix to x_matrix.

This function should not be called for  DST  which  is  attached  to  SRC
(opposite situation, when SRC is attached to DST, is possible).

Depending on situation, following actions are performed 
* for SRC attached to DST, this function performs no actions (no need  to
  do anything)
* for independent matrices of different sizes it allocates storage in DST
  and copy contents of SRC  to  DST.  DST->last_action field  is  set  to
  ACT_NEW_LOCATION, and DST->owner is set to OWN_AE.
* for  independent  matrices  of  same  sizes  it does not perform memory
  (re)allocation.  It  just  copies  SRC  to  already   existing   place.
  DST->last_action   is   set   to    ACT_SAME_LOCATION  (unless  it  was
  ACT_NEW_LOCATION), DST->owner is unmodified.

dst                 destination vector
src                 source, matrix in x-format
state               ALGLIB environment state

NOTES:
* dst is assumed to be initialized. Its contents is freed before  copying
  data  from src  (if  size / type  are  different)  or  overwritten  (if
  possible given destination size).
************************************************************************/
void ae_x_set_matrix(x_matrix *dst, ae_matrix *src, ae_state *state)
{
    char *p_src_row;
    char *p_dst_row;
    ae_int_t i;
    ae_int_t row_size;
    if( src->ptr.pp_void!=NULL && src->ptr.pp_void[0] == dst->ptr )
    {
        /* src->ptr points to the beginning of dst, attached matrices, no need to copy */
        return;
    }
    if( dst->rows!=src->rows || dst->cols!=src->cols || dst->datatype!=src->datatype )
    {
        if( dst->owner==OWN_AE )
            ae_free(dst->ptr);
        dst->rows = src->rows;
        dst->cols = src->cols;
        dst->stride = src->cols;
        dst->datatype = src->datatype;
        dst->ptr = ae_malloc((size_t)(dst->rows*((ae_int_t)dst->stride)*ae_sizeof(src->datatype)), state);
        if( dst->rows!=0 && dst->stride!=0 && dst->ptr==NULL )
            ae_break(state, ERR_OUT_OF_MEMORY, "ae_malloc(): out of memory");
        dst->last_action = ACT_NEW_LOCATION;
        dst->owner = OWN_AE;
    }
    else
    {
        if( dst->last_action==ACT_UNCHANGED )
            dst->last_action = ACT_SAME_LOCATION;
        else if( dst->last_action==ACT_SAME_LOCATION )
            dst->last_action = ACT_SAME_LOCATION;
        else if( dst->last_action==ACT_NEW_LOCATION )
            dst->last_action = ACT_NEW_LOCATION;
        else
            ae_assert(ae_false, "ALGLIB: internal error in ae_x_set_vector()", state);
    }
    if( src->rows!=0 && src->cols!=0 )
    {
        p_src_row = (char*)(src->ptr.pp_void[0]);
        p_dst_row = (char*)dst->ptr;
        row_size = ae_sizeof(src->datatype)*src->cols;
        for(i=0; i<src->rows; i++, p_src_row+=src->stride*ae_sizeof(src->datatype), p_dst_row+=dst->stride*ae_sizeof(src->datatype))
            memcpy(p_dst_row, p_src_row, (size_t)(row_size));
    }
}

/************************************************************************
This function attaches x_vector to ae_vector's contents.
Ownership of memory allocated is not changed (it is still managed by
ae_matrix).

dst                 destination vector
src                 source, vector in x-format
state               ALGLIB environment state

NOTES:
* dst is assumed to be initialized. Its contents is freed before
  attaching to src.
* this function doesn't need ae_state parameter because it can't fail
  (assuming correctly initialized src)
************************************************************************/
void ae_x_attach_to_vector(x_vector *dst, ae_vector *src)
{
    if( dst->owner==OWN_AE )
        ae_free(dst->ptr);
    dst->ptr = src->ptr.p_ptr;
    dst->last_action = ACT_NEW_LOCATION;
    dst->cnt = src->cnt;
    dst->datatype = src->datatype;
    dst->owner = OWN_CALLER;
}

/************************************************************************
This function attaches x_matrix to ae_matrix's contents.
Ownership of memory allocated is not changed (it is still managed by
ae_matrix).

dst                 destination vector
src                 source, matrix in x-format
state               ALGLIB environment state

NOTES:
* dst is assumed to be initialized. Its contents is freed before
  attaching to src.
* this function doesn't need ae_state parameter because it can't fail
  (assuming correctly initialized src)
************************************************************************/
void ae_x_attach_to_matrix(x_matrix *dst, ae_matrix *src)
{
    if( dst->owner==OWN_AE )
            ae_free(dst->ptr);
    dst->rows = src->rows;
    dst->cols = src->cols;
    dst->stride = src->stride;
    dst->datatype = src->datatype;
    dst->ptr = &(src->ptr.pp_double[0][0]);
    dst->last_action = ACT_NEW_LOCATION;
    dst->owner = OWN_CALLER;
}

/************************************************************************
This function clears x_vector. It does nothing  if vector is not owned by
ALGLIB environment.

dst                 vector
************************************************************************/
void x_vector_clear(x_vector *dst)
{
    if( dst->owner==OWN_AE )
        aligned_free(dst->ptr);
    dst->ptr = NULL;
    dst->cnt = 0;
}

/************************************************************************
Assertion
************************************************************************/
void ae_assert(ae_bool cond, const char *msg, ae_state *state)
{
    if( !cond )
        ae_break(state, ERR_ASSERTION_FAILED, msg);
}

/************************************************************************
CPUID

Returns information about features CPU and compiler support.

You must tell ALGLIB what CPU family is used by defining AE_CPU symbol
(without this hint zero will be returned).

Note: results of this function depend on both CPU and compiler;
if compiler doesn't support SSE intrinsics, function won't set 
corresponding flag.
************************************************************************/
static volatile ae_bool _ae_cpuid_initialized = ae_false;
static volatile ae_bool _ae_cpuid_has_sse2 = ae_false;
ae_int_t ae_cpuid()
{
    /*
     * to speed up CPU detection we cache results from previous attempts
     * there is no synchronization, but it is still thread safe.
     *
     * thread safety is guaranteed on all modern architectures which
     * have following property: simultaneous writes by different cores
     * to the same location will be executed in serial manner.
     *
     */
    ae_int_t result;
    
    /*
     * if not initialized, determine system properties
     */
    if( !_ae_cpuid_initialized )
    {
        /*
         * SSE2
         */
#if defined(AE_CPU)
#if (AE_CPU==AE_INTEL) && defined(AE_HAS_SSE2_INTRINSICS)
#if AE_COMPILER==AE_MSVC
        {
            int CPUInfo[4];
            __cpuid(CPUInfo, 1);
            if( (CPUInfo[3]&0x04000000)!=0 )
                _ae_cpuid_has_sse2 = ae_true;
        }
#elif AE_COMPILER==AE_GNUC
        {
            ae_int_t a,b,c,d;
            __asm__ __volatile__ ("cpuid": "=a" (a), "=b" (b), "=c" (c), "=d" (d) : "a" (1));
            if( (d&0x04000000)!=0 )
                _ae_cpuid_has_sse2 = ae_true;
        }
#elif AE_COMPILER==AE_SUNC
        {
            ae_int_t a,b,c,d;
            __asm__ __volatile__ ("cpuid": "=a" (a), "=b" (b), "=c" (c), "=d" (d) : "a" (1));
            if( (d&0x04000000)!=0 )
                _ae_cpuid_has_sse2 = ae_true;
        }
#else
#endif
#endif
#endif
        /*
         * set initialization flag
         */
        _ae_cpuid_initialized = ae_true;
    }
    
    /*
     * return
     */
    result = 0;
    if( _ae_cpuid_has_sse2 )
        result = result|CPU_SSE2;
    return result;
}

/************************************************************************
Real math functions
************************************************************************/
ae_bool ae_fp_eq(double v1, double v2)
{
    /* IEEE-strict floating point comparison */
    volatile double x = v1;
    volatile double y = v2;
    return x==y;
}

ae_bool ae_fp_neq(double v1, double v2)
{
    /* IEEE-strict floating point comparison */
    return !ae_fp_eq(v1,v2);
}

ae_bool ae_fp_less(double v1, double v2)
{
    /* IEEE-strict floating point comparison */
    volatile double x = v1;
    volatile double y = v2;
    return x<y;
}

ae_bool ae_fp_less_eq(double v1, double v2)
{
    /* IEEE-strict floating point comparison */
    volatile double x = v1;
    volatile double y = v2;
    return x<=y;
}

ae_bool ae_fp_greater(double v1, double v2)
{
    /* IEEE-strict floating point comparison */
    volatile double x = v1;
    volatile double y = v2;
    return x>y;
}

ae_bool ae_fp_greater_eq(double v1, double v2)
{
    /* IEEE-strict floating point comparison */
    volatile double x = v1;
    volatile double y = v2;
    return x>=y;
}

ae_bool ae_isfinite_stateless(double x, ae_int_t endianness)
{
    union _u
    {
        double a;
        ae_int32_t p[2];
    } u;
    ae_int32_t high;
    u.a = x;
    if( endianness==AE_LITTLE_ENDIAN )
        high = u.p[1];
    else
        high = u.p[0];
    return (high & (ae_int32_t)0x7FF00000)!=(ae_int32_t)0x7FF00000;
}

ae_bool ae_isnan_stateless(double x,    ae_int_t endianness)
{
    union _u
    {
        double a;
        ae_int32_t p[2];
    } u;
    ae_int32_t high, low;
    u.a = x;
    if( endianness==AE_LITTLE_ENDIAN )
    {
        high = u.p[1];
        low =  u.p[0];
    }
    else
    {
        high = u.p[0];
        low =  u.p[1];
    }
    return ((high &0x7FF00000)==0x7FF00000) && (((high &0x000FFFFF)!=0) || (low!=0));
}

ae_bool ae_isinf_stateless(double x,    ae_int_t endianness)
{
    union _u
    {
        double a;
        ae_int32_t p[2];
    } u;
    ae_int32_t high, low;
    u.a = x;
    if( endianness==AE_LITTLE_ENDIAN )
    {
        high = u.p[1];
        low  = u.p[0];
    }
    else
    {
        high = u.p[0];
        low  = u.p[1];
    }
    
    /* 31 least significant bits of high are compared */
    return ((high&0x7FFFFFFF)==0x7FF00000) && (low==0); 
}

ae_bool ae_isposinf_stateless(double x, ae_int_t endianness)
{
    union _u
    {
        double a;
        ae_int32_t p[2];
    } u;
    ae_int32_t high, low;
    u.a = x;
    if( endianness==AE_LITTLE_ENDIAN )
    {
        high = u.p[1];
        low  = u.p[0];
    }
    else
    {
        high = u.p[0];
        low  = u.p[1];
    }
    
    /* all 32 bits of high are compared */
    return (high==(ae_int32_t)0x7FF00000) && (low==0); 
}

ae_bool ae_isneginf_stateless(double x, ae_int_t endianness)
{
    union _u
    {
        double a;
        ae_int32_t p[2];
    } u;
    ae_int32_t high, low;
    u.a = x;
    if( endianness==AE_LITTLE_ENDIAN )
    {
        high = u.p[1];
        low  = u.p[0];
    }
    else
    {
        high = u.p[0];
        low  = u.p[1];
    }
    
    /* this code is a bit tricky to avoid comparison of high with 0xFFF00000, which may be unsafe with some buggy compilers */
    return ((high&0x7FFFFFFF)==0x7FF00000) && (high!=(ae_int32_t)0x7FF00000) && (low==0);
}

ae_int_t ae_get_endianness()
{
    union
    {
        double a;
        ae_int32_t p[2];
    } u;
    
    /*
     * determine endianness
     * two types are supported: big-endian and little-endian.
     * mixed-endian hardware is NOT supported.
     *
     * 1983 is used as magic number because its non-periodic double 
     * representation allow us to easily distinguish between upper 
     * and lower halfs and to detect mixed endian hardware.
     *
     */
    u.a = 1.0/1983.0; 
    if( u.p[1]==(ae_int32_t)0x3f408642 )
        return AE_LITTLE_ENDIAN;
    if( u.p[0]==(ae_int32_t)0x3f408642 )
        return AE_BIG_ENDIAN;
    return AE_MIXED_ENDIAN;
}

ae_bool ae_isfinite(double x,ae_state *state)
{
    return ae_isfinite_stateless(x, state->endianness);
}

ae_bool ae_isnan(double x,   ae_state *state)
{
    return ae_isnan_stateless(x, state->endianness);
}

ae_bool ae_isinf(double x,   ae_state *state)
{
    return ae_isinf_stateless(x, state->endianness);
}

ae_bool ae_isposinf(double x,ae_state *state)
{
    return ae_isposinf_stateless(x, state->endianness);
}

ae_bool ae_isneginf(double x,ae_state *state)
{
    return ae_isneginf_stateless(x, state->endianness);
}

double ae_fabs(double x,  ae_state *state)
{
    return fabs(x);
}

ae_int_t ae_iabs(ae_int_t x, ae_state *state)
{
    return x>=0 ? x : -x;
}

double ae_sqr(double x,  ae_state *state)
{
    return x*x;
}

double ae_sqrt(double x, ae_state *state)
{
    return sqrt(x);
}

ae_int_t ae_sign(double x, ae_state *state)
{
    if( x>0 ) return  1;
    if( x<0 ) return -1;
    return 0;
}

ae_int_t ae_round(double x, ae_state *state)
{
    return (ae_int_t)(ae_ifloor(x+0.5,state));
}

ae_int_t ae_trunc(double x, ae_state *state)
{
    return (ae_int_t)(x>0 ? ae_ifloor(x,state) : ae_iceil(x,state));
}

ae_int_t ae_ifloor(double x, ae_state *state)
{
    return (ae_int_t)(floor(x));
}

ae_int_t ae_iceil(double x,  ae_state *state)
{
    return (ae_int_t)(ceil(x));
}

ae_int_t ae_maxint(ae_int_t m1, ae_int_t m2, ae_state *state)
{
    return m1>m2 ? m1 : m2;
}

ae_int_t ae_minint(ae_int_t m1, ae_int_t m2, ae_state *state)
{
    return m1>m2 ? m2 : m1;
}

double ae_maxreal(double m1, double m2, ae_state *state)
{
    return m1>m2 ? m1 : m2;
}

double ae_minreal(double m1, double m2, ae_state *state)
{
    return m1>m2 ? m2 : m1;
}

double ae_randomreal(ae_state *state)
{
    int i1 = rand();
    int i2 = rand();
    double mx = (double)(RAND_MAX)+1.0;
    volatile double tmp0 = i2/mx;
    volatile double tmp1 = i1+tmp0;
    return tmp1/mx;
}

ae_int_t ae_randominteger(ae_int_t maxv, ae_state *state)
{
    return rand()%maxv;
}

double   ae_sin(double x, ae_state *state)
{
    return sin(x);
}

double   ae_cos(double x, ae_state *state)
{
    return cos(x);
}

double   ae_tan(double x, ae_state *state)
{
    return tan(x);
}

double   ae_sinh(double x, ae_state *state)
{
    return sinh(x);
}

double   ae_cosh(double x, ae_state *state)
{
    return cosh(x);
}
double   ae_tanh(double x, ae_state *state)
{
    return tanh(x);
}

double   ae_asin(double x, ae_state *state)
{
    return asin(x);
}

double   ae_acos(double x, ae_state *state)
{
    return acos(x);
}

double   ae_atan(double x, ae_state *state)
{
    return atan(x);
}

double   ae_atan2(double y, double x, ae_state *state)
{
    return atan2(y,x);
}

double   ae_log(double x, ae_state *state)
{
    return log(x);
}

double   ae_pow(double x, double y, ae_state *state)
{
    return pow(x,y);
}

double   ae_exp(double x, ae_state *state)
{
    return exp(x);
}

/************************************************************************
Symmetric/Hermitian properties: check and force
************************************************************************/
static void x_split_length(ae_int_t n, ae_int_t nb, ae_int_t* n1, ae_int_t* n2)
{
    ae_int_t r;
    if( n<=nb )
    {
        *n1 = n;
        *n2 = 0;
    }
    else
    {
        if( n%nb!=0 )
        {
            *n2 = n%nb;
            *n1 = n-(*n2);
        }
        else
        {
            *n2 = n/2;
            *n1 = n-(*n2);
            if( *n1%nb==0 )
            {
                return;
            }
            r = nb-*n1%nb;
            *n1 = *n1+r;
            *n2 = *n2-r;
        }
    }
}
static double x_safepythag2(double x, double y)
{
    double w;
    double xabs;
    double yabs;
    double z;
    xabs = fabs(x);
    yabs = fabs(y);
    w = xabs>yabs ? xabs : yabs;
    z = xabs<yabs ? xabs : yabs;
    if( z==0 )
        return w;
    else
    {
        double t;
        t = z/w;
        return w*sqrt(1+t*t);
    }
}
/*
 * this function checks difference between offdiagonal blocks BL and BU
 * (see below). Block BL is specified by offsets (offset0,offset1)  and
 * sizes (len0,len1).
 *
 *     [ .          ]
 *     [   A0  BU   ]
 * A = [   BL  A1   ]
 *     [          . ]
 *
 *  this subroutine updates current values of:
 *  a) mx       maximum value of A[i,j] found so far
 *  b) err      componentwise difference between elements of BL and BU^T
 *
 */
static void is_symmetric_rec_off_stat(x_matrix *a, ae_int_t offset0, ae_int_t offset1, ae_int_t len0, ae_int_t len1, ae_bool *nonfinite, double *mx, double *err, ae_state *_state)
{
    /* try to split problem into two smaller ones */
    if( len0>x_nb || len1>x_nb )
    {
        ae_int_t n1, n2;
        if( len0>len1 )
        {
            x_split_length(len0, x_nb, &n1, &n2);
            is_symmetric_rec_off_stat(a, offset0,    offset1, n1, len1, nonfinite, mx, err, _state);
            is_symmetric_rec_off_stat(a, offset0+n1, offset1, n2, len1, nonfinite, mx, err, _state);
        }
        else
        {
            x_split_length(len1, x_nb, &n1, &n2);
            is_symmetric_rec_off_stat(a, offset0, offset1,    len0, n1, nonfinite, mx, err, _state);
            is_symmetric_rec_off_stat(a, offset0, offset1+n1, len0, n2, nonfinite, mx, err, _state);
        }
        return;
    }
    else
    {
        /* base case */
        double *p1, *p2, *prow, *pcol;
        double v;
        ae_int_t i, j;

        p1 = (double*)(a->ptr)+offset0*a->stride+offset1;
        p2 = (double*)(a->ptr)+offset1*a->stride+offset0;
        for(i=0; i<len0; i++)
        {
            pcol = p2+i;
            prow = p1+i*a->stride;
            for(j=0; j<len1; j++)
            {
                if( !ae_isfinite(*pcol,_state) || !ae_isfinite(*prow,_state) )
                {
                    *nonfinite = ae_true;
                }
                else
                {
                    v = fabs(*pcol);
                    *mx =  *mx>v ? *mx : v;
                    v = fabs(*prow);
                    *mx =  *mx>v ? *mx : v;
                    v = fabs(*pcol-*prow);
                    *err = *err>v ? *err : v;
                }                
                pcol += a->stride;
                prow++;
            }
        }
    }
}
/*
 * this function checks that diagonal block A0 is symmetric.
 * Block A0 is specified by its offset and size.
 *
 *     [ .          ]
 *     [   A0       ]
 * A = [       .    ]
 *     [          . ]
 *
 *  this subroutine updates current values of:
 *  a) mx       maximum value of A[i,j] found so far
 *  b) err      componentwise difference between A0 and A0^T
 *
 */
static void is_symmetric_rec_diag_stat(x_matrix *a, ae_int_t offset, ae_int_t len, ae_bool *nonfinite, double *mx, double *err, ae_state *_state)
{
    double *p, *prow, *pcol;
    double v;
    ae_int_t i, j;
    
    /* try to split problem into two smaller ones */
    if( len>x_nb )
    {
        ae_int_t n1, n2;
        x_split_length(len, x_nb, &n1, &n2);
        is_symmetric_rec_diag_stat(a, offset, n1, nonfinite, mx, err, _state);
        is_symmetric_rec_diag_stat(a, offset+n1, n2, nonfinite, mx, err, _state);
        is_symmetric_rec_off_stat(a, offset+n1, offset, n2, n1, nonfinite, mx, err, _state);
        return;
    }
    
    /* base case */
    p = (double*)(a->ptr)+offset*a->stride+offset;
    for(i=0; i<len; i++)
    {
        pcol = p+i;
        prow = p+i*a->stride;
        for(j=0; j<i; j++,pcol+=a->stride,prow++)
        {
            if( !ae_isfinite(*pcol,_state) || !ae_isfinite(*prow,_state) )
            {
                *nonfinite = ae_true;
            }
            else
            {
                v = fabs(*pcol);
                *mx =  *mx>v ? *mx : v;
                v = fabs(*prow);
                *mx =  *mx>v ? *mx : v;
                v = fabs(*pcol-*prow);
                *err = *err>v ? *err : v;
            }
        }
        v = fabs(p[i+i*a->stride]);
        *mx =  *mx>v ? *mx : v;
    }
}
/*
 * this function checks difference between offdiagonal blocks BL and BU
 * (see below). Block BL is specified by offsets (offset0,offset1)  and
 * sizes (len0,len1).
 *
 *     [ .          ]
 *     [   A0  BU   ]
 * A = [   BL  A1   ]
 *     [          . ]
 *
 *  this subroutine updates current values of:
 *  a) mx       maximum value of A[i,j] found so far
 *  b) err      componentwise difference between elements of BL and BU^H
 *
 */
static void is_hermitian_rec_off_stat(x_matrix *a, ae_int_t offset0, ae_int_t offset1, ae_int_t len0, ae_int_t len1, ae_bool *nonfinite, double *mx, double *err, ae_state *_state)
{
    /* try to split problem into two smaller ones */
    if( len0>x_nb || len1>x_nb )
    {
        ae_int_t n1, n2;
        if( len0>len1 )
        {
            x_split_length(len0, x_nb, &n1, &n2);
            is_hermitian_rec_off_stat(a, offset0,    offset1, n1, len1, nonfinite, mx, err, _state);
            is_hermitian_rec_off_stat(a, offset0+n1, offset1, n2, len1, nonfinite, mx, err, _state);
        }
        else
        {
            x_split_length(len1, x_nb, &n1, &n2);
            is_hermitian_rec_off_stat(a, offset0, offset1,    len0, n1, nonfinite, mx, err, _state);
            is_hermitian_rec_off_stat(a, offset0, offset1+n1, len0, n2, nonfinite, mx, err, _state);
        }
        return;
    }
    else
    {
        /* base case */
        ae_complex *p1, *p2, *prow, *pcol;
        double v;
        ae_int_t i, j;

        p1 = (ae_complex*)(a->ptr)+offset0*a->stride+offset1;
        p2 = (ae_complex*)(a->ptr)+offset1*a->stride+offset0;
        for(i=0; i<len0; i++)
        {
            pcol = p2+i;
            prow = p1+i*a->stride;
            for(j=0; j<len1; j++)
            {
                if( !ae_isfinite(pcol->x, _state) || !ae_isfinite(pcol->y, _state) || !ae_isfinite(prow->x, _state) || !ae_isfinite(prow->y, _state) )
                {
                    *nonfinite = ae_true;
                }
                else
                {
                    v = x_safepythag2(pcol->x, pcol->y);
                    *mx =  *mx>v ? *mx : v;
                    v = x_safepythag2(prow->x, prow->y);
                    *mx =  *mx>v ? *mx : v;
                    v = x_safepythag2(pcol->x-prow->x, pcol->y+prow->y);
                    *err = *err>v ? *err : v;
                }
                pcol += a->stride;
                prow++;
            }
        }
    }
}
/*
 * this function checks that diagonal block A0 is Hermitian.
 * Block A0 is specified by its offset and size.
 *
 *     [ .          ]
 *     [   A0       ]
 * A = [       .    ]
 *     [          . ]
 *
 *  this subroutine updates current values of:
 *  a) mx       maximum value of A[i,j] found so far
 *  b) err      componentwise difference between A0 and A0^H
 *
 */
static void is_hermitian_rec_diag_stat(x_matrix *a, ae_int_t offset, ae_int_t len, ae_bool *nonfinite, double *mx, double *err, ae_state *_state)
{
    ae_complex *p, *prow, *pcol;
    double v;
    ae_int_t i, j;
    
    /* try to split problem into two smaller ones */
    if( len>x_nb )
    {
        ae_int_t n1, n2;
        x_split_length(len, x_nb, &n1, &n2);
        is_hermitian_rec_diag_stat(a, offset, n1, nonfinite, mx, err, _state);
        is_hermitian_rec_diag_stat(a, offset+n1, n2, nonfinite, mx, err, _state);
        is_hermitian_rec_off_stat(a, offset+n1, offset, n2, n1, nonfinite, mx, err, _state);
        return;
    }
    
    /* base case */
    p = (ae_complex*)(a->ptr)+offset*a->stride+offset;
    for(i=0; i<len; i++)
    {
        pcol = p+i;
        prow = p+i*a->stride;
        for(j=0; j<i; j++,pcol+=a->stride,prow++)
        {
            if( !ae_isfinite(pcol->x, _state) || !ae_isfinite(pcol->y, _state) || !ae_isfinite(prow->x, _state) || !ae_isfinite(prow->y, _state) )
            {
                *nonfinite = ae_true;
            }
            else
            {
                v = x_safepythag2(pcol->x, pcol->y);
                *mx =  *mx>v ? *mx : v;
                v = x_safepythag2(prow->x, prow->y);
                *mx =  *mx>v ? *mx : v;
                v = x_safepythag2(pcol->x-prow->x, pcol->y+prow->y);
                *err = *err>v ? *err : v;
            }
        }
        if( !ae_isfinite(p[i+i*a->stride].x, _state) || !ae_isfinite(p[i+i*a->stride].y, _state) )
        {
            *nonfinite = ae_true;
        }
        else
        {
            v = fabs(p[i+i*a->stride].x);
            *mx =  *mx>v ? *mx : v;
            v = fabs(p[i+i*a->stride].y);
            *err =  *err>v ? *err : v;
        }
    }
}
/*
 * this function copies offdiagonal block BL to its symmetric counterpart
 * BU (see below). Block BL is specified by offsets (offset0,offset1)
 * and sizes (len0,len1).
 *
 *     [ .          ]
 *     [   A0  BU   ]
 * A = [   BL  A1   ]
 *     [          . ]
 *
 */
static void force_symmetric_rec_off_stat(x_matrix *a, ae_int_t offset0, ae_int_t offset1, ae_int_t len0, ae_int_t len1)
{
    /* try to split problem into two smaller ones */
    if( len0>x_nb || len1>x_nb )
    {
        ae_int_t n1, n2;
        if( len0>len1 )
        {
            x_split_length(len0, x_nb, &n1, &n2);
            force_symmetric_rec_off_stat(a, offset0,    offset1, n1, len1);
            force_symmetric_rec_off_stat(a, offset0+n1, offset1, n2, len1);
        }
        else
        {
            x_split_length(len1, x_nb, &n1, &n2);
            force_symmetric_rec_off_stat(a, offset0, offset1,    len0, n1);
            force_symmetric_rec_off_stat(a, offset0, offset1+n1, len0, n2);
        }
        return;
    }
    else
    {
        /* base case */
        double *p1, *p2, *prow, *pcol;
        ae_int_t i, j;

        p1 = (double*)(a->ptr)+offset0*a->stride+offset1;
        p2 = (double*)(a->ptr)+offset1*a->stride+offset0;
        for(i=0; i<len0; i++)
        {
            pcol = p2+i;
            prow = p1+i*a->stride;
            for(j=0; j<len1; j++)
            {
                *pcol = *prow;
                pcol += a->stride;
                prow++;
            }
        }
    }
}
/*
 * this function copies lower part of diagonal block A0 to its upper part
 * Block is specified by offset and size.
 *
 *     [ .          ]
 *     [   A0       ]
 * A = [       .    ]
 *     [          . ]
 *
 */
static void force_symmetric_rec_diag_stat(x_matrix *a, ae_int_t offset, ae_int_t len)
{
    double *p, *prow, *pcol;
    ae_int_t i, j;
    
    /* try to split problem into two smaller ones */
    if( len>x_nb )
    {
        ae_int_t n1, n2;
        x_split_length(len, x_nb, &n1, &n2);
        force_symmetric_rec_diag_stat(a, offset, n1);
        force_symmetric_rec_diag_stat(a, offset+n1, n2);
        force_symmetric_rec_off_stat(a, offset+n1, offset, n2, n1);
        return;
    }
    
    /* base case */
    p = (double*)(a->ptr)+offset*a->stride+offset;
    for(i=0; i<len; i++)
    {
        pcol = p+i;
        prow = p+i*a->stride;
        for(j=0; j<i; j++,pcol+=a->stride,prow++)
            *pcol = *prow;
    }
}
/*
 * this function copies Hermitian transpose of offdiagonal block BL to
 * its symmetric counterpart BU (see below). Block BL is specified by
 * offsets (offset0,offset1) and sizes (len0,len1).
 *
 *     [ .          ]
 *     [   A0  BU   ]
 * A = [   BL  A1   ]
 *     [          . ]
 */
static void force_hermitian_rec_off_stat(x_matrix *a, ae_int_t offset0, ae_int_t offset1, ae_int_t len0, ae_int_t len1)
{
    /* try to split problem into two smaller ones */
    if( len0>x_nb || len1>x_nb )
    {
        ae_int_t n1, n2;
        if( len0>len1 )
        {
            x_split_length(len0, x_nb, &n1, &n2);
            force_hermitian_rec_off_stat(a, offset0,    offset1, n1, len1);
            force_hermitian_rec_off_stat(a, offset0+n1, offset1, n2, len1);
        }
        else
        {
            x_split_length(len1, x_nb, &n1, &n2);
            force_hermitian_rec_off_stat(a, offset0, offset1,    len0, n1);
            force_hermitian_rec_off_stat(a, offset0, offset1+n1, len0, n2);
        }
        return;
    }
    else
    {
        /* base case */
        ae_complex *p1, *p2, *prow, *pcol;
        ae_int_t i, j;

        p1 = (ae_complex*)(a->ptr)+offset0*a->stride+offset1;
        p2 = (ae_complex*)(a->ptr)+offset1*a->stride+offset0;
        for(i=0; i<len0; i++)
        {
            pcol = p2+i;
            prow = p1+i*a->stride;
            for(j=0; j<len1; j++)
            {
                *pcol = *prow;
                pcol += a->stride;
                prow++;
            }
        }
    }
}
/*
 * this function copies Hermitian transpose of lower part of
 * diagonal block A0 to its upper part Block is specified by offset and size.
 *
 *     [ .          ]
 *     [   A0       ]
 * A = [       .    ]
 *     [          . ]
 *
 */
static void force_hermitian_rec_diag_stat(x_matrix *a, ae_int_t offset, ae_int_t len)
{
    ae_complex *p, *prow, *pcol;
    ae_int_t i, j;
    
    /* try to split problem into two smaller ones */
    if( len>x_nb )
    {
        ae_int_t n1, n2;
        x_split_length(len, x_nb, &n1, &n2);
        force_hermitian_rec_diag_stat(a, offset, n1);
        force_hermitian_rec_diag_stat(a, offset+n1, n2);
        force_hermitian_rec_off_stat(a, offset+n1, offset, n2, n1);
        return;
    }
    
    /* base case */
    p = (ae_complex*)(a->ptr)+offset*a->stride+offset;
    for(i=0; i<len; i++)
    {
        pcol = p+i;
        prow = p+i*a->stride;
        for(j=0; j<i; j++,pcol+=a->stride,prow++)
            *pcol = *prow;
    }
}
ae_bool x_is_symmetric(x_matrix *a)
{
    double mx, err;
    ae_bool nonfinite;
    ae_state _alglib_env_state;
    if( a->datatype!=DT_REAL )
        return ae_false;
    if( a->cols!=a->rows )
        return ae_false;
    if( a->cols==0 || a->rows==0 )
        return ae_true;
    ae_state_init(&_alglib_env_state);
    mx = 0;
    err = 0;
    nonfinite = ae_false;
    is_symmetric_rec_diag_stat(a, 0, (ae_int_t)a->rows, &nonfinite, &mx, &err, &_alglib_env_state);
    if( nonfinite )
        return ae_false;
    if( mx==0 )
        return ae_true;
    return err/mx<=1.0E-14;
}
ae_bool x_is_hermitian(x_matrix *a)
{
    double mx, err;
    ae_bool nonfinite;
    ae_state _alglib_env_state;
    if( a->datatype!=DT_COMPLEX )
        return ae_false;
    if( a->cols!=a->rows )
        return ae_false;
    if( a->cols==0 || a->rows==0 )
        return ae_true;
    ae_state_init(&_alglib_env_state);
    mx = 0;
    err = 0;
    nonfinite = ae_false;
    is_hermitian_rec_diag_stat(a, 0, (ae_int_t)a->rows, &nonfinite, &mx, &err, &_alglib_env_state);
    if( nonfinite )
        return ae_false;
    if( mx==0 )
        return ae_true;
    return err/mx<=1.0E-14;
}
ae_bool x_force_symmetric(x_matrix *a)
{
    if( a->datatype!=DT_REAL )
        return ae_false;
    if( a->cols!=a->rows )
        return ae_false;
    if( a->cols==0 || a->rows==0 )
        return ae_true;
    force_symmetric_rec_diag_stat(a, 0, (ae_int_t)a->rows);
    return ae_true;
}
ae_bool x_force_hermitian(x_matrix *a)
{
    if( a->datatype!=DT_COMPLEX )
        return ae_false;
    if( a->cols!=a->rows )
        return ae_false;
    if( a->cols==0 || a->rows==0 )
        return ae_true;
    force_hermitian_rec_diag_stat(a, 0, (ae_int_t)a->rows);
    return ae_true;
}

ae_bool ae_is_symmetric(ae_matrix *a)
{
    x_matrix x;
    x.owner = OWN_CALLER;
    ae_x_attach_to_matrix(&x, a);
    return x_is_symmetric(&x);
}

ae_bool ae_is_hermitian(ae_matrix *a)
{
    x_matrix x;
    x.owner = OWN_CALLER;
    ae_x_attach_to_matrix(&x, a);
    return x_is_hermitian(&x);
}

ae_bool ae_force_symmetric(ae_matrix *a)
{
    x_matrix x;
    x.owner = OWN_CALLER;
    ae_x_attach_to_matrix(&x, a);
    return x_force_symmetric(&x);
}

ae_bool ae_force_hermitian(ae_matrix *a)
{
    x_matrix x;
    x.owner = OWN_CALLER;
    ae_x_attach_to_matrix(&x, a);
    return x_force_hermitian(&x);
}

/************************************************************************
This function converts six-bit value (from 0 to 63)  to  character  (only
digits, lowercase and uppercase letters, minus and underscore are used).

If v is negative or greater than 63, this function returns '?'.
************************************************************************/
static char _sixbits2char_tbl[64] = { 
        '0', '1', '2', '3', '4', '5', '6', '7',
        '8', '9', 'A', 'B', 'C', 'D', 'E', 'F',
        'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N',
        'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V',
        'W', 'X', 'Y', 'Z', 'a', 'b', 'c', 'd', 
        'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 
        'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 
        'u', 'v', 'w', 'x', 'y', 'z', '-', '_' };

char ae_sixbits2char(ae_int_t v)
{
    
    if( v<0 || v>63 )
        return '?';
    return _sixbits2char_tbl[v]; 
    
    /* v is correct, process it */
    /*if( v<10 )
        return '0'+v;
    v -= 10;
    if( v<26 )
        return 'A'+v;
    v -= 26;
    if( v<26 )
        return 'a'+v;
    v -= 26;
    return v==0 ? '-' : '_';*/
}

/************************************************************************
This function converts character to six-bit value (from 0 to 63).

This function is inverse of ae_sixbits2char()
If c is not correct character, this function returns -1.
************************************************************************/
static ae_int_t _ae_char2sixbits_tbl[] = {
    -1, -1, -1, -1, -1, -1, -1, -1,
    -1, -1, -1, -1, -1, -1, -1, -1,
    -1, -1, -1, -1, -1, -1, -1, -1,
    -1, -1, -1, -1, -1, -1, -1, -1,
    -1, -1, -1, -1, -1, -1, -1, -1,
    -1, -1, -1, -1, -1, 62, -1, -1,
     0,  1,  2,  3,  4,  5,  6,  7,
     8,  9, -1, -1, -1, -1, -1, -1,
    -1, 10, 11, 12, 13, 14, 15, 16,
    17, 18, 19, 20, 21, 22, 23, 24,
    25, 26, 27, 28, 29, 30, 31, 32,
    33, 34, 35, -1, -1, -1, -1, 63,
    -1, 36, 37, 38, 39, 40, 41, 42,
    43, 44, 45, 46, 47, 48, 49, 50,
    51, 52, 53, 54, 55, 56, 57, 58,
    59, 60, 61, -1, -1, -1, -1, -1 };
ae_int_t ae_char2sixbits(char c)
{
    return (c>=0 && c<127) ? _ae_char2sixbits_tbl[(int)c] : -1;
}

/************************************************************************
This function converts three bytes (24 bits) to four six-bit values 
(24 bits again).

src     pointer to three bytes
dst     pointer to four ints
************************************************************************/
void ae_threebytes2foursixbits(const unsigned char *src, ae_int_t *dst)
{
    dst[0] = src[0] & 0x3F;
    dst[1] = (src[0]>>6) | ((src[1]&0x0F)<<2);
    dst[2] = (src[1]>>4) | ((src[2]&0x03)<<4);
    dst[3] = src[2]>>2;
}

/************************************************************************
This function converts four six-bit values (24 bits) to three bytes
(24 bits again).

src     pointer to four ints
dst     pointer to three bytes
************************************************************************/
void ae_foursixbits2threebytes(const ae_int_t *src, unsigned char *dst)
{
    dst[0] = (unsigned char)(     src[0] | ((src[1]&0x03)<<6));
    dst[1] = (unsigned char)((src[1]>>2) | ((src[2]&0x0F)<<4));
    dst[2] = (unsigned char)((src[2]>>4) | (src[3]<<2));
}

/************************************************************************
This function serializes boolean value into buffer

v           boolean value to be serialized
buf         buffer, at least 12 characters wide 
            (11 chars for value, one for trailing zero)
state       ALGLIB environment state
************************************************************************/
void ae_bool2str(ae_bool v, char *buf, ae_state *state)
{
    char c = v ? '1' : '0';
    ae_int_t i;
    for(i=0; i<AE_SER_ENTRY_LENGTH; i++)
        buf[i] = c;
    buf[AE_SER_ENTRY_LENGTH] = 0;
}

/************************************************************************
This function unserializes boolean value from buffer

buf         buffer which contains value; leading spaces/tabs/newlines are 
            ignored, traling spaces/tabs/newlines are treated as  end  of
            the boolean value.
state       ALGLIB environment state

This function raises an error in case unexpected symbol is found
************************************************************************/
ae_bool ae_str2bool(const char *buf, ae_state *state, const char **pasttheend)
{
    ae_bool was0, was1;
    const char *emsg = "ALGLIB: unable to read boolean value from stream";
    
    was0 = ae_false;
    was1 = ae_false;
    while( *buf==' ' || *buf=='\t' || *buf=='\n' || *buf=='\r' )
        buf++;
    while( *buf!=' ' && *buf!='\t' && *buf!='\n' && *buf!='\r' && *buf!=0 )
    {
        if( *buf=='0' )
        {
            was0 = ae_true;
            buf++;
            continue;
        }
        if( *buf=='1' )
        {
            was1 = ae_true;
            buf++;
            continue;
        }
        ae_break(state, ERR_ASSERTION_FAILED, emsg);
    }
    *pasttheend = buf;
    if( (!was0) && (!was1) )
        ae_break(state, ERR_ASSERTION_FAILED, emsg);
    if( was0 && was1 )
        ae_break(state, ERR_ASSERTION_FAILED, emsg);
    return was1 ? ae_true : ae_false;
}

/************************************************************************
This function serializes integer value into buffer

v           integer value to be serialized
buf         buffer, at least 12 characters wide 
            (11 chars for value, one for trailing zero)
state       ALGLIB environment state
************************************************************************/
void ae_int2str(ae_int_t v, char *buf, ae_state *state)
{
    union _u
    {
        ae_int_t ival;
        unsigned char bytes[9];
    } u;
    ae_int_t i;
    ae_int_t sixbits[12];
    unsigned char c;
    
    /*
     * copy v to array of chars, sign extending it and 
     * converting to little endian order
     *
     * because we don't want to mention size of ae_int_t explicitly, 
     * we do it as follows:
     * 1. we fill u.bytes by zeros or ones (depending on sign of v)
     * 2. we copy v to u.ival
     * 3. if we run on big endian architecture, we reorder u.bytes
     * 4. now we have signed 64-bit representation of v stored in u.bytes
     * 5. additionally, we set 9th byte of u.bytes to zero in order to
     *    simplify conversion to six-bit representation
     */
    c = v<0 ? (unsigned char)0xFF : (unsigned char)0x00;
    u.ival = v;
    for(i=sizeof(ae_int_t); i<=8; i++) /* <=8 is preferred because it avoids unnecessary compiler warnings*/
        u.bytes[i] = c;
    u.bytes[8] = 0;
    if( state->endianness==AE_BIG_ENDIAN )
    {
        for(i=0; i<(ae_int_t)(sizeof(ae_int_t)/2); i++)
        {
            unsigned char tc;
            tc = u.bytes[i];
            u.bytes[i] = u.bytes[sizeof(ae_int_t)-1-i];
            u.bytes[sizeof(ae_int_t)-1-i] = tc;
        }
    }
    
    /*
     * convert to six-bit representation, output
     *
     * NOTE: last 12th element of sixbits is always zero, we do not output it
     */
    ae_threebytes2foursixbits(u.bytes+0, sixbits+0);
    ae_threebytes2foursixbits(u.bytes+3, sixbits+4);
    ae_threebytes2foursixbits(u.bytes+6, sixbits+8);        
    for(i=0; i<AE_SER_ENTRY_LENGTH; i++)
        buf[i] = ae_sixbits2char(sixbits[i]);
    buf[AE_SER_ENTRY_LENGTH] = 0x00;
}

/************************************************************************
This function unserializes integer value from string

buf         buffer which contains value; leading spaces/tabs/newlines are 
            ignored, traling spaces/tabs/newlines are treated as  end  of
            the boolean value.
state       ALGLIB environment state

This function raises an error in case unexpected symbol is found
************************************************************************/
ae_int_t ae_str2int(const char *buf, ae_state *state, const char **pasttheend)
{
    const char *emsg = "ALGLIB: unable to read integer value from stream";
    ae_int_t sixbits[12];
    ae_int_t sixbitsread, i;
    union _u
    {
        ae_int_t ival;
        unsigned char bytes[9];
    } u;
    /* 
     * 1. skip leading spaces
     * 2. read and decode six-bit digits
     * 3. set trailing digits to zeros
     * 4. convert to little endian 64-bit integer representation
     * 5. convert to big endian representation, if needed
     */
    while( *buf==' ' || *buf=='\t' || *buf=='\n' || *buf=='\r' )
        buf++;
    sixbitsread = 0;
    while( *buf!=' ' && *buf!='\t' && *buf!='\n' && *buf!='\r' && *buf!=0 )
    {
        ae_int_t d;
        d = ae_char2sixbits(*buf);
        if( d<0 || sixbitsread>=AE_SER_ENTRY_LENGTH )
            ae_break(state, ERR_ASSERTION_FAILED, emsg);
        sixbits[sixbitsread] = d;
        sixbitsread++;
        buf++;
    }
    *pasttheend = buf;
    if( sixbitsread==0 )
        ae_break(state, ERR_ASSERTION_FAILED, emsg);
    for(i=sixbitsread; i<12; i++)
        sixbits[i] = 0;
    ae_foursixbits2threebytes(sixbits+0, u.bytes+0);
    ae_foursixbits2threebytes(sixbits+4, u.bytes+3);
    ae_foursixbits2threebytes(sixbits+8, u.bytes+6);
    if( state->endianness==AE_BIG_ENDIAN )
    {
        for(i=0; i<(ae_int_t)(sizeof(ae_int_t)/2); i++)
        {
            unsigned char tc;
            tc = u.bytes[i];
            u.bytes[i] = u.bytes[sizeof(ae_int_t)-1-i];
            u.bytes[sizeof(ae_int_t)-1-i] = tc;
        }
    }
    return u.ival;
}


/************************************************************************
This function serializes double value into buffer

v           double value to be serialized
buf         buffer, at least 12 characters wide 
            (11 chars for value, one for trailing zero)
state       ALGLIB environment state
************************************************************************/
void ae_double2str(double v, char *buf, ae_state *state)
{
    union _u
    {
        double dval;
        unsigned char bytes[9];
    } u;
    ae_int_t i;
    ae_int_t sixbits[12];

    /*
     * handle special quantities
     */
    if( ae_isnan(v, state) )
    {
        const char *s = ".nan_______";
        memcpy(buf, s, strlen(s)+1);
        return;
    }
    if( ae_isposinf(v, state) )
    {
        const char *s = ".posinf____";
        memcpy(buf, s, strlen(s)+1);
        return;
    }
    if( ae_isneginf(v, state) )
    {
        const char *s = ".neginf____";
        memcpy(buf, s, strlen(s)+1);
        return;
    }
    
    /*
     * process general case:
     * 1. copy v to array of chars
     * 2. set 9th byte of u.bytes to zero in order to
     *    simplify conversion to six-bit representation
     * 3. convert to little endian (if needed)
     * 4. convert to six-bit representation
     *    (last 12th element of sixbits is always zero, we do not output it)
     */
    u.dval = v;
    u.bytes[8] = 0;
    if( state->endianness==AE_BIG_ENDIAN )
    {
        for(i=0; i<(ae_int_t)(sizeof(double)/2); i++)
        {
            unsigned char tc;
            tc = u.bytes[i];
            u.bytes[i] = u.bytes[sizeof(double)-1-i];
            u.bytes[sizeof(double)-1-i] = tc;
        }
    }
    ae_threebytes2foursixbits(u.bytes+0, sixbits+0);
    ae_threebytes2foursixbits(u.bytes+3, sixbits+4);
    ae_threebytes2foursixbits(u.bytes+6, sixbits+8);
    for(i=0; i<AE_SER_ENTRY_LENGTH; i++)
        buf[i] = ae_sixbits2char(sixbits[i]);
    buf[AE_SER_ENTRY_LENGTH] = 0x00;
}

/************************************************************************
This function unserializes double value from string

buf         buffer which contains value; leading spaces/tabs/newlines are 
            ignored, traling spaces/tabs/newlines are treated as  end  of
            the boolean value.
state       ALGLIB environment state

This function raises an error in case unexpected symbol is found
************************************************************************/
double ae_str2double(const char *buf, ae_state *state, const char **pasttheend)
{
    const char *emsg = "ALGLIB: unable to read double value from stream";
    ae_int_t sixbits[12];
    ae_int_t sixbitsread, i;
    union _u
    {
        double dval;
        unsigned char bytes[9];
    } u;
    
    
     /* 
      * skip leading spaces
      */
    while( *buf==' ' || *buf=='\t' || *buf=='\n' || *buf=='\r' )
        buf++;
      
    /*
     * Handle special cases
     */
    if( *buf=='.' )
    {
        const char *s_nan =    ".nan_______";
        const char *s_posinf = ".posinf____";
        const char *s_neginf = ".neginf____";
        if( strncmp(buf, s_nan, strlen(s_nan))==0 )
        {
            *pasttheend = buf+strlen(s_nan);
            return state->v_nan;
        }
        if( strncmp(buf, s_posinf, strlen(s_posinf))==0 )
        {
            *pasttheend = buf+strlen(s_posinf);
            return state->v_posinf;
        }
        if( strncmp(buf, s_neginf, strlen(s_neginf))==0 )
        {
            *pasttheend = buf+strlen(s_neginf);
            return state->v_neginf;
        }
        ae_break(state, ERR_ASSERTION_FAILED, emsg);
    }
    
    /* 
     * General case:
     * 1. read and decode six-bit digits
     * 2. check that all 11 digits were read
     * 3. set last 12th digit to zero (needed for simplicity of conversion)
     * 4. convert to 8 bytes
     * 5. convert to big endian representation, if needed
     */
    sixbitsread = 0;
    while( *buf!=' ' && *buf!='\t' && *buf!='\n' && *buf!='\r' && *buf!=0 )
    {
        ae_int_t d;
        d = ae_char2sixbits(*buf);
        if( d<0 || sixbitsread>=AE_SER_ENTRY_LENGTH )
            ae_break(state, ERR_ASSERTION_FAILED, emsg);
        sixbits[sixbitsread] = d;
        sixbitsread++;
        buf++;
    }
    *pasttheend = buf;
    if( sixbitsread!=AE_SER_ENTRY_LENGTH )
        ae_break(state, ERR_ASSERTION_FAILED, emsg);
    sixbits[AE_SER_ENTRY_LENGTH] = 0;
    ae_foursixbits2threebytes(sixbits+0, u.bytes+0);
    ae_foursixbits2threebytes(sixbits+4, u.bytes+3);
    ae_foursixbits2threebytes(sixbits+8, u.bytes+6);
    if( state->endianness==AE_BIG_ENDIAN )
    {
        for(i=0; i<(ae_int_t)(sizeof(double)/2); i++)
        {
            unsigned char tc;
            tc = u.bytes[i];
            u.bytes[i] = u.bytes[sizeof(double)-1-i];
            u.bytes[sizeof(double)-1-i] = tc;
        }
    }
    return u.dval;
}


/************************************************************************
This function performs given number of spin-wait iterations
************************************************************************/
void ae_spin_wait(ae_int_t cnt)
{
    /*
     * these strange operations with ae_never_change_it are necessary to
     * prevent compiler optimization of the loop.
     */
    volatile ae_int_t i;
    
    /* very unlikely because no one will wait for such amount of cycles */
    if( cnt>0x12345678 )
        ae_never_change_it = cnt%10;
    
    /* spin wait, test condition which will never be true */
    for(i=0; i<cnt; i++)
        if( ae_never_change_it>0 )
            ae_never_change_it--;
}


/************************************************************************
This function causes the calling thread to relinquish the CPU. The thread
is moved to the end of the queue and some other thread gets to run.

NOTE: this function should NOT be called when AE_OS is AE_UNKNOWN  -  the
      whole program will be abnormally terminated.
************************************************************************/
void ae_yield()
{
#if AE_OS==AE_WINDOWS
    if( !SwitchToThread() )
        Sleep(0);
#elif AE_OS==AE_POSIX
    sched_yield();
#else
    abort();
#endif
}

/************************************************************************
This function initializes ae_lock structure and sets lock in a free mode.
************************************************************************/
void ae_init_lock(ae_lock *lock)
{
    _lock *p;
    lock->ptr = malloc(sizeof(_lock));
    AE_CRITICAL_ASSERT(lock->ptr!=NULL);
    p = (_lock*)lock->ptr;
#if AE_OS==AE_WINDOWS
    p->p_lock = (ae_int_t*)ae_align((void*)(&p->buf),AE_LOCK_ALIGNMENT);
    p->p_lock[0] = 0;
#elif AE_OS==AE_POSIX
    pthread_mutex_init(&p->mutex, NULL);
#else
    p->is_locked = ae_false;
#endif
}


/************************************************************************
This function acquires lock. In case lock is busy, we perform several
iterations inside tight loop before trying again.
************************************************************************/
void ae_acquire_lock(ae_lock *lock)
{
#if AE_OS==AE_WINDOWS
    ae_int_t cnt = 0;
#endif
    _lock *p;
    p = (_lock*)lock->ptr;
#if AE_OS==AE_WINDOWS
#ifdef AE_SMP_DEBUGCOUNTERS
    InterlockedIncrement((LONG volatile *)&_ae_dbg_lock_acquisitions);
#endif
    for(;;)
    {
		if( InterlockedCompareExchange((LONG volatile *)p->p_lock, 1, 0)==0 )
		    return;
        ae_spin_wait(AE_LOCK_CYCLES);
#ifdef AE_SMP_DEBUGCOUNTERS
        InterlockedIncrement((LONG volatile *)&_ae_dbg_lock_spinwaits);
#endif
        cnt++;
        if( cnt%AE_LOCK_TESTS_BEFORE_YIELD==0 )
        {
#ifdef AE_SMP_DEBUGCOUNTERS
            InterlockedIncrement((LONG volatile *)&_ae_dbg_lock_yields);
#endif
            ae_yield();
        }
    }
#elif AE_OS==AE_POSIX
    ae_int_t cnt = 0;
    for(;;)
    {
		if(  pthread_mutex_trylock(&p->mutex)==0 )
		    return;
        ae_spin_wait(AE_LOCK_CYCLES);
        cnt++;
        if( cnt%AE_LOCK_TESTS_BEFORE_YIELD==0 )
            ae_yield();
    }
   ;
#else
    AE_CRITICAL_ASSERT(!p->is_locked);
    p->is_locked = ae_true;
#endif
}


/************************************************************************
This function releases lock.
************************************************************************/
void ae_release_lock(ae_lock *lock)
{
    _lock *p;
    p = (_lock*)lock->ptr;
#if AE_OS==AE_WINDOWS
    InterlockedExchange((LONG volatile *)p->p_lock, 0);
#elif AE_OS==AE_POSIX
    pthread_mutex_unlock(&p->mutex);
#else
    p->is_locked = ae_false;
#endif
}


/************************************************************************
This function frees ae_lock structure.
************************************************************************/
void ae_free_lock(ae_lock *lock)
{
    _lock *p;
    p = (_lock*)lock->ptr;
#if AE_OS==AE_POSIX
    pthread_mutex_destroy(&p->mutex);
#endif
    free(p);
}


/************************************************************************
This function creates ae_shared_pool structure.

dst                 destination shared pool;
                    already allocated, but not initialized.
state               ALGLIB environment state
make_automatic      if true, pool is added to the dynamic block list

Error handling:
* if state is NULL, returns ae_false on allocation error
* if state is not NULL, calls ae_break() on allocation error
* returns ae_true on success

dst is assumed to be uninitialized, its fields are ignored.
************************************************************************/
ae_bool ae_shared_pool_init(void *_dst, ae_state *state, ae_bool make_automatic)
{
    ae_shared_pool *dst;
    
    dst = (ae_shared_pool*)_dst;
    
    /* init */
    dst->seed_object = NULL;
    dst->recycled_objects = NULL;
    dst->recycled_entries = NULL;
    dst->enumeration_counter = NULL;
    dst->size_of_object = 0;
    dst->init = NULL;
    dst->init_copy = NULL;
    dst->destroy = NULL;
    dst->frame_entry.deallocator = ae_shared_pool_destroy;
    dst->frame_entry.ptr = dst;
    if( make_automatic && state!=NULL )
        ae_db_attach(&dst->frame_entry, state);
    ae_init_lock(&dst->pool_lock);
    return ae_true;
}


/************************************************************************
This function clears all dynamically allocated fields of the pool except
for the lock. It does NOT try to acquire pool_lock.

NOTE: this function is NOT thread-safe, it is not protected by lock.
************************************************************************/
static void ae_shared_pool_internalclear(ae_shared_pool *dst)
{
    ae_shared_pool_entry *ptr, *tmp;
    
    /* destroy seed */
    if( dst->seed_object!=NULL )
    {
        dst->destroy((void*)dst->seed_object);
        ae_free((void*)dst->seed_object);
        dst->seed_object = NULL;
    }
    
    /* destroy recycled objects */
    for(ptr=dst->recycled_objects; ptr!=NULL;)
    {
        tmp = (ae_shared_pool_entry*)ptr->next_entry;
        dst->destroy(ptr->obj);
        ae_free(ptr->obj);
        ae_free(ptr);
        ptr = tmp;
    }
    dst->recycled_objects = NULL;
    
    /* destroy recycled entries */
    for(ptr=dst->recycled_entries; ptr!=NULL;)
    {
        tmp = (ae_shared_pool_entry*)ptr->next_entry;
        ae_free(ptr);
        ptr = tmp;
    }
    dst->recycled_entries = NULL;
}


/************************************************************************
This function creates copy of ae_shared_pool.

dst                 destination pool, allocated but not initialized
src                 source pool
state               ALGLIB environment state
make_automatic      if true, pool is added to the dynamic block list

Error handling:
* if state is NULL, returns ae_false on allocation error
* if state is not NULL, calls ae_break() on allocation error
* returns ae_true on success

dst is assumed to be uninitialized, its fields are ignored.

NOTE: this function is NOT thread-safe. It does not acquire pool lock, so
      you should NOT call it when lock can be used by another thread.
************************************************************************/
ae_bool ae_shared_pool_init_copy(void *_dst, void *_src, ae_state *state, ae_bool make_automatic)
{
    ae_shared_pool *dst, *src;
    ae_shared_pool_entry *ptr;
    
    /* state!=NULL, allocation errors result in exception */
    AE_CRITICAL_ASSERT(state!=NULL);
    
    dst = (ae_shared_pool*)_dst;
    src = (ae_shared_pool*)_src;
    if( !ae_shared_pool_init(dst, state, make_automatic) )
        return ae_false;
    
    /* copy non-pointer fields */
    dst->size_of_object = src->size_of_object;
    dst->init = src->init;
    dst->init_copy = src->init_copy;
    dst->destroy = src->destroy;
    ae_init_lock(&dst->pool_lock);    
    
    /* copy seed object */
    if( src->seed_object!=NULL )
    {
        dst->seed_object = ae_malloc(dst->size_of_object, state);
        if( !dst->init_copy(dst->seed_object, src->seed_object, state, ae_false) )
            return ae_false;
    }
    
    /* copy recycled objects */
    dst->recycled_objects = NULL;
    for(ptr=src->recycled_objects; ptr!=NULL; ptr=(ae_shared_pool_entry*)ptr->next_entry)
    {
        ae_shared_pool_entry *tmp;
        tmp = (ae_shared_pool_entry*)ae_malloc(sizeof(ae_shared_pool_entry), state);
        tmp->obj =  ae_malloc(dst->size_of_object, state);
        if( !dst->init_copy(tmp->obj, ptr->obj, state, ae_false) )
            return ae_false;
        tmp->next_entry = dst->recycled_objects;
        dst->recycled_objects = tmp;
    }
    
    /* recycled entries are not copied because they do not store any information */
    dst->recycled_entries = NULL;
    
    /* enumeration counter is reset on copying */
    dst->enumeration_counter = NULL;
    
    /* initialize frame record */
    dst->frame_entry.deallocator = ae_shared_pool_destroy;
    dst->frame_entry.ptr = dst;
    
    /* return */
    return ae_true;
}


/************************************************************************
This function clears contents of the pool, but pool remain usable.

IMPORTANT: this function invalidates dst, it can not be used after it  is
           cleared.

NOTE: this function is NOT thread-safe. It does not acquire pool lock, so
      you should NOT call it when lock can be used by another thread.
************************************************************************/
void ae_shared_pool_clear(void *_dst)
{
    ae_shared_pool *dst = (ae_shared_pool*)_dst;
    
    /* clear seed and lists */
    ae_shared_pool_internalclear(dst);
    
    /* clear fields */
    dst->seed_object = NULL;
    dst->recycled_objects = NULL;
    dst->recycled_entries = NULL;
    dst->enumeration_counter = NULL;
    dst->size_of_object = 0;
    dst->init = NULL;
    dst->init_copy = NULL;
    dst->destroy = NULL;
}


/************************************************************************
This function destroys  pool  (object  is  left  in  invalid  state,  all
dynamically allocated memory is freed).

NOTE: this function is NOT thread-safe. It does not acquire pool lock, so
      you should NOT call it when lock can be used by another thread.
************************************************************************/
void ae_shared_pool_destroy(void *_dst)
{
    ae_shared_pool *dst = (ae_shared_pool*)_dst;
    ae_shared_pool_clear(_dst);
    ae_free_lock(&dst->pool_lock);
}


/************************************************************************
This function returns True, if internal seed object was set.  It  returns
False for un-seeded pool.

dst                 destination pool (initialized by constructor function)

NOTE: this function is NOT thread-safe. It does not acquire pool lock, so
      you should NOT call it when lock can be used by another thread.
************************************************************************/
ae_bool ae_shared_pool_is_initialized(void *_dst)
{
    ae_shared_pool *dst = (ae_shared_pool*)_dst;
    return dst->seed_object!=NULL;
}


/************************************************************************
This function sets internal seed object. All objects owned by the pool
(current seed object, recycled objects) are automatically freed.

dst                 destination pool (initialized by constructor function)
seed_object         new seed object
size_of_object      sizeof(), used to allocate memory
init                constructor function
init_copy           copy constructor
clear               destructor function
state               ALGLIB environment state

NOTE: this function is NOT thread-safe. It does not acquire pool lock, so
      you should NOT call it when lock can be used by another thread.
************************************************************************/
void ae_shared_pool_set_seed(
    ae_shared_pool  *dst,
    void            *seed_object,
    ae_int_t        size_of_object,
    ae_bool         (*init)(void* dst, ae_state* state, ae_bool make_automatic),
    ae_bool         (*init_copy)(void* dst, void* src, ae_state* state, ae_bool make_automatic),
    void            (*destroy)(void* ptr),
    ae_state        *state)
{
    /* state!=NULL, allocation errors result in exception */
    AE_CRITICAL_ASSERT(state!=NULL);
    
    /* destroy internal objects */
    ae_shared_pool_internalclear(dst);
    
    /* set non-pointer fields */
    dst->size_of_object = size_of_object;
    dst->init = init;
    dst->init_copy = init_copy;
    dst->destroy = destroy;
    
    /* set seed object */
    dst->seed_object = ae_malloc(size_of_object, state);
    ae_assert(
        init_copy(dst->seed_object, seed_object, state, ae_false),
        "ALGLIB: unable to initialize seed in ae_shared_pool_set_seed()",
        state);
}


/************************************************************************
This  function  retrieves  a  copy  of  the seed object from the pool and
stores it to target smart pointer ptr.

In case target pointer owns non-NULL  value,  it  is  deallocated  before
storing value retrieved from pool. Target pointer becomes  owner  of  the
value which was retrieved from pool.

pool                pool
pptr                pointer to ae_smart_ptr structure
state               ALGLIB environment state

NOTE: this function IS thread-safe.  It  acquires  pool  lock  during its
      operation and can be used simultaneously from several threads.
************************************************************************/
void ae_shared_pool_retrieve(
    ae_shared_pool  *pool,
    ae_smart_ptr    *pptr,
    ae_state        *state)
{
    void *new_obj;
    
    /* state!=NULL, allocation errors are handled by throwing exception from ae_malloc() */
    AE_CRITICAL_ASSERT(state!=NULL);
    
    /* assert that pool was seeded */
    ae_assert(
        pool->seed_object!=NULL,
        "ALGLIB: shared pool is not seeded, PoolRetrieve() failed",
        state);
    
    /* acquire lock */
    ae_acquire_lock(&pool->pool_lock);
    
    /* try to reuse recycled objects */
    if( pool->recycled_objects!=NULL )
    {
        void *new_obj;
        ae_shared_pool_entry *result;
        
        /* retrieve entry/object from list of recycled objects */
        result = pool->recycled_objects;
        pool->recycled_objects = (ae_shared_pool_entry*)pool->recycled_objects->next_entry;
        new_obj = result->obj;
        result->obj = NULL;
        
        /* move entry to list of recycled entries */
        result->next_entry = pool->recycled_entries;
        pool->recycled_entries = result;
        
        /* release lock */
        ae_release_lock(&pool->pool_lock);
        
        /* assign object to smart pointer */
        ae_smart_ptr_assign(pptr, new_obj, ae_true, ae_true, pool->destroy);
        return;
    }
        
    /* release lock; we do not need it anymore because copy constructor does not modify source variable */
    ae_release_lock(&pool->pool_lock);
    
    /* create new object from seed */
    new_obj = ae_malloc(pool->size_of_object, state);
    ae_assert(
        pool->init_copy(new_obj, pool->seed_object, state, ae_false),
        "ALGLIB: unable to initialize object in ae_shared_pool_retrieve()",
        state);
        
    /* assign object to smart pointer and return */
    ae_smart_ptr_assign(pptr, new_obj, ae_true, ae_true, pool->destroy);
}


/************************************************************************
This function recycles object owned by smart  pointer  by  moving  it  to
internal storage of the shared pool.

Source pointer must own the object. After function is over, it owns NULL
pointer.

pool                pool
pptr                pointer to ae_smart_ptr structure
state               ALGLIB environment state

NOTE: this function IS thread-safe.  It  acquires  pool  lock  during its
      operation and can be used simultaneously from several threads.
************************************************************************/
void ae_shared_pool_recycle(
    ae_shared_pool  *pool,
    ae_smart_ptr    *pptr,
    ae_state        *state)
{
    ae_shared_pool_entry *new_entry;
    
    /* state!=NULL, allocation errors are handled by throwing exception from ae_malloc() */
    AE_CRITICAL_ASSERT(state!=NULL);
    
    /* assert that pool was seeded */
    ae_assert(
        pool->seed_object!=NULL,
        "ALGLIB: shared pool is not seeded, PoolRecycle() failed",
        state);
    
    /* assert that pointer non-null and owns the object */
    ae_assert(pptr->is_owner,  "ALGLIB: pptr in ae_shared_pool_recycle() does not own its pointer", state);
    ae_assert(pptr->ptr!=NULL, "ALGLIB: pptr in ae_shared_pool_recycle() is NULL", state);
    
    /* acquire lock */
    ae_acquire_lock(&pool->pool_lock);
    
    /* acquire shared pool entry (reuse one from recycled_entries or malloc new one) */
    if( pool->recycled_entries!=NULL )
    {
        /* reuse previously allocated entry */
        new_entry = pool->recycled_entries;
        pool->recycled_entries = (ae_shared_pool_entry*)new_entry->next_entry;
    }
    else
    {
        /*
         * Allocate memory for new entry.
         *
         * NOTE: we release pool lock during allocation because ae_malloc() may raise
         *       exception and we do not want our pool to be left in the locked state.
         */
        ae_release_lock(&pool->pool_lock);
        new_entry =  (ae_shared_pool_entry*)ae_malloc(sizeof(ae_shared_pool_entry), state);
        ae_acquire_lock(&pool->pool_lock);
    }
    
    /* add object to the list of recycled objects */
    new_entry->obj = pptr->ptr;
    new_entry->next_entry = pool->recycled_objects;
    pool->recycled_objects = new_entry;
    
    /* release lock object */
    ae_release_lock(&pool->pool_lock);
    
    /* release source pointer */
    ae_smart_ptr_release(pptr);
}


/************************************************************************
This function clears internal list of  recycled  objects,  but  does  not
change seed object managed by the pool.

pool                pool
state               ALGLIB environment state

NOTE: this function is NOT thread-safe. It does not acquire pool lock, so
      you should NOT call it when lock can be used by another thread.
************************************************************************/
void ae_shared_pool_clear_recycled(
    ae_shared_pool  *pool,
    ae_state        *state)
{
    ae_shared_pool_entry *ptr, *tmp;
    
    /* clear recycled objects */
    for(ptr=pool->recycled_objects; ptr!=NULL;)
    {
        tmp = (ae_shared_pool_entry*)ptr->next_entry;
        pool->destroy(ptr->obj);
        ae_free(ptr->obj);
        ae_free(ptr);
        ptr = tmp;
    }
    pool->recycled_objects = NULL;
}


/************************************************************************
This function allows to enumerate recycled elements of the  shared  pool.
It stores pointer to the first recycled object in the smart pointer.

IMPORTANT:
* in case target pointer owns non-NULL  value,  it  is deallocated before
  storing value retrieved from pool.
* recycled object IS NOT removed from pool
* target pointer DOES NOT become owner of the new value
* this function IS NOT thread-safe
* you SHOULD NOT modify shared pool during enumeration (although you  can
  modify state of the objects retrieved from pool)
* in case there is no recycled objects in the pool, NULL is stored to pptr
* in case pool is not seeded, NULL is stored to pptr

pool                pool
pptr                pointer to ae_smart_ptr structure
state               ALGLIB environment state
************************************************************************/
void ae_shared_pool_first_recycled(
    ae_shared_pool  *pool,
    ae_smart_ptr    *pptr,
    ae_state        *state)
{   
    /* modify internal enumeration counter */
    pool->enumeration_counter = pool->recycled_objects;
    
    /* exit on empty list */
    if( pool->enumeration_counter==NULL )
    {
        ae_smart_ptr_assign(pptr, NULL, ae_false, ae_false, NULL);
        return;
    }
    
    /* assign object to smart pointer */
    ae_smart_ptr_assign(pptr, pool->enumeration_counter->obj, ae_false, ae_false, pool->destroy);
}


/************************************************************************
This function allows to enumerate recycled elements of the  shared  pool.
It stores pointer to the next recycled object in the smart pointer.

IMPORTANT:
* in case target pointer owns non-NULL  value,  it  is deallocated before
  storing value retrieved from pool.
* recycled object IS NOT removed from pool
* target pointer DOES NOT become owner of the new value
* this function IS NOT thread-safe
* you SHOULD NOT modify shared pool during enumeration (although you  can
  modify state of the objects retrieved from pool)
* in case there is no recycled objects left in the pool, NULL is stored.
* in case pool is not seeded, NULL is stored.

pool                pool
pptr                pointer to ae_smart_ptr structure
state               ALGLIB environment state
************************************************************************/
void ae_shared_pool_next_recycled(
    ae_shared_pool  *pool,
    ae_smart_ptr    *pptr,
    ae_state        *state)
{   
    /* exit on end of list */
    if( pool->enumeration_counter==NULL )
    {
        ae_smart_ptr_assign(pptr, NULL, ae_false, ae_false, NULL);
        return;
    }
    
    /* modify internal enumeration counter */
    pool->enumeration_counter = (ae_shared_pool_entry*)pool->enumeration_counter->next_entry;
    
    /* exit on empty list */
    if( pool->enumeration_counter==NULL )
    {
        ae_smart_ptr_assign(pptr, NULL, ae_false, ae_false, NULL);
        return;
    }
    
    /* assign object to smart pointer */
    ae_smart_ptr_assign(pptr, pool->enumeration_counter->obj, ae_false, ae_false, pool->destroy);
}



/************************************************************************
This function clears internal list of recycled objects and  seed  object.
However, pool still can be used (after initialization with another seed).

pool                pool
state               ALGLIB environment state

NOTE: this function is NOT thread-safe. It does not acquire pool lock, so
      you should NOT call it when lock can be used by another thread.
************************************************************************/
void ae_shared_pool_reset(
    ae_shared_pool  *pool,
    ae_state        *state)
{
    /* clear seed and lists */
    ae_shared_pool_internalclear(pool);
    
    /* clear fields */
    pool->seed_object = NULL;
    pool->recycled_objects = NULL;
    pool->recycled_entries = NULL;
    pool->enumeration_counter = NULL;
    pool->size_of_object = 0;
    pool->init = NULL;
    pool->init_copy = NULL;
    pool->destroy = NULL;
}


/************************************************************************
This function initializes serializer
************************************************************************/
void ae_serializer_init(ae_serializer *serializer)
{
    serializer->mode = AE_SM_DEFAULT;
    serializer->entries_needed = 0;
    serializer->bytes_asked = 0;
}

void ae_serializer_clear(ae_serializer *serializer)
{
}

void ae_serializer_alloc_start(ae_serializer *serializer)
{
    serializer->entries_needed = 0;
    serializer->bytes_asked = 0;
    serializer->mode = AE_SM_ALLOC;
}

void ae_serializer_alloc_entry(ae_serializer *serializer)
{
    serializer->entries_needed++;
}

ae_int_t ae_serializer_get_alloc_size(ae_serializer *serializer)
{
    ae_int_t rows, lastrowsize, result;
    
    serializer->mode = AE_SM_READY2S;
    
    /* if no entries needes (degenerate case) */
    if( serializer->entries_needed==0 )
    {
        serializer->bytes_asked = 1;
        return serializer->bytes_asked;
    }
    
    /* non-degenerate case */
    rows = serializer->entries_needed/AE_SER_ENTRIES_PER_ROW;
    lastrowsize = AE_SER_ENTRIES_PER_ROW;
    if( serializer->entries_needed%AE_SER_ENTRIES_PER_ROW )
    {
        lastrowsize = serializer->entries_needed%AE_SER_ENTRIES_PER_ROW;
        rows++;
    }
    
    /* calculate result size */
    result  = ((rows-1)*AE_SER_ENTRIES_PER_ROW+lastrowsize)*AE_SER_ENTRY_LENGTH;
    result +=  (rows-1)*(AE_SER_ENTRIES_PER_ROW-1)+(lastrowsize-1);
    result += rows*2;
    serializer->bytes_asked = result;
    return result;
}

#ifdef AE_USE_CPP_SERIALIZATION
void ae_serializer_sstart_str(ae_serializer *serializer, std::string *buf)
{
    serializer->mode = AE_SM_TO_CPPSTRING;
    serializer->out_cppstr = buf;
    serializer->entries_saved = 0;
    serializer->bytes_written = 0;
}
#endif

#ifdef AE_USE_CPP_SERIALIZATION
void ae_serializer_ustart_str(ae_serializer *serializer, const std::string *buf)
{
    serializer->mode = AE_SM_FROM_STRING;
    serializer->in_str = buf->c_str();
}
#endif

void ae_serializer_sstart_str(ae_serializer *serializer, char *buf)
{
    serializer->mode = AE_SM_TO_STRING;
    serializer->out_str = buf;
    serializer->out_str[0] = 0;
    serializer->entries_saved = 0;
    serializer->bytes_written = 0;
}

void ae_serializer_ustart_str(ae_serializer *serializer, const char *buf)
{
    serializer->mode = AE_SM_FROM_STRING;
    serializer->in_str = buf;
}

void ae_serializer_serialize_bool(ae_serializer *serializer, ae_bool v, ae_state *state)
{
    char buf[AE_SER_ENTRY_LENGTH+2+1];
    const char *emsg = "ALGLIB: serialization integrity error";
    ae_int_t bytes_appended;
    
    /* prepare serialization, check consistency */
    ae_bool2str(v, buf, state);
    serializer->entries_saved++;
    if( serializer->entries_saved%AE_SER_ENTRIES_PER_ROW )
        strcat(buf, " ");
    else
        strcat(buf, "\r\n");
    bytes_appended = (ae_int_t)strlen(buf);
    if( serializer->bytes_written+bytes_appended > serializer->bytes_asked )
        ae_break(state, ERR_ASSERTION_FAILED, emsg);
    serializer->bytes_written += bytes_appended;
        
    /* append to buffer */
#ifdef AE_USE_CPP_SERIALIZATION
    if( serializer->mode==AE_SM_TO_CPPSTRING )
    {
        *(serializer->out_cppstr) += buf;
        return;
    }
#endif
    if( serializer->mode==AE_SM_TO_STRING )
    {
        strcat(serializer->out_str, buf);
        serializer->out_str += bytes_appended;
        return;
    }
    ae_break(state, ERR_ASSERTION_FAILED, emsg);
}

void ae_serializer_serialize_int(ae_serializer *serializer, ae_int_t v, ae_state *state)
{
    char buf[AE_SER_ENTRY_LENGTH+2+1];
    const char *emsg = "ALGLIB: serialization integrity error";
    ae_int_t bytes_appended;
    
    /* prepare serialization, check consistency */
    ae_int2str(v, buf, state);
    serializer->entries_saved++;
    if( serializer->entries_saved%AE_SER_ENTRIES_PER_ROW )
        strcat(buf, " ");
    else
        strcat(buf, "\r\n");
    bytes_appended = (ae_int_t)strlen(buf);
    if( serializer->bytes_written+bytes_appended > serializer->bytes_asked )
        ae_break(state, ERR_ASSERTION_FAILED, emsg);
    serializer->bytes_written += bytes_appended;
        
    /* append to buffer */
#ifdef AE_USE_CPP_SERIALIZATION
    if( serializer->mode==AE_SM_TO_CPPSTRING )
    {
        *(serializer->out_cppstr) += buf;
        return;
    }
#endif
    if( serializer->mode==AE_SM_TO_STRING )
    {
        strcat(serializer->out_str, buf);
        serializer->out_str += bytes_appended;
        return;
    }
    ae_break(state, ERR_ASSERTION_FAILED, emsg);
}

void ae_serializer_serialize_double(ae_serializer *serializer, double v, ae_state *state)
{
    char buf[AE_SER_ENTRY_LENGTH+2+1];
    const char *emsg = "ALGLIB: serialization integrity error";
    ae_int_t bytes_appended;
    
    /* prepare serialization, check consistency */
    ae_double2str(v, buf, state);
    serializer->entries_saved++;
    if( serializer->entries_saved%AE_SER_ENTRIES_PER_ROW )
        strcat(buf, " ");
    else
        strcat(buf, "\r\n");
    bytes_appended = (ae_int_t)strlen(buf);
    if( serializer->bytes_written+bytes_appended > serializer->bytes_asked )
        ae_break(state, ERR_ASSERTION_FAILED, emsg);
    serializer->bytes_written += bytes_appended;
        
    /* append to buffer */
#ifdef AE_USE_CPP_SERIALIZATION
    if( serializer->mode==AE_SM_TO_CPPSTRING )
    {
        *(serializer->out_cppstr) += buf;
        return;
    }
#endif
    if( serializer->mode==AE_SM_TO_STRING )
    {
        strcat(serializer->out_str, buf);
        serializer->out_str += bytes_appended;
        return;
    }
    ae_break(state, ERR_ASSERTION_FAILED, emsg);
}

void ae_serializer_unserialize_bool(ae_serializer *serializer, ae_bool *v, ae_state *state)
{
    *v = ae_str2bool(serializer->in_str, state, &serializer->in_str);
}

void ae_serializer_unserialize_int(ae_serializer *serializer, ae_int_t *v, ae_state *state)
{
    *v = ae_str2int(serializer->in_str, state, &serializer->in_str);
}

void ae_serializer_unserialize_double(ae_serializer *serializer, double *v, ae_state *state)
{
    *v = ae_str2double(serializer->in_str, state, &serializer->in_str);
}

void ae_serializer_stop(ae_serializer *serializer)
{
}


/************************************************************************
Complex math functions
************************************************************************/
ae_complex ae_complex_from_d(double v)
{
    ae_complex r;
    r.x = v;
    r.y = 0.0;
    return r;
}

ae_complex ae_c_neg(ae_complex lhs)
{
    ae_complex result;
    result.x = -lhs.x;
    result.y = -lhs.y;
    return result;
}

ae_complex ae_c_conj(ae_complex lhs, ae_state *state)
{
    ae_complex result;
    result.x = +lhs.x;
    result.y = -lhs.y;
    return result;
}

ae_complex ae_c_sqr(ae_complex lhs, ae_state *state)
{
    ae_complex result;
    result.x = lhs.x*lhs.x-lhs.y*lhs.y;
    result.y = 2*lhs.x*lhs.y;
    return result;
}

double ae_c_abs(ae_complex z, ae_state *state)
{
    double w;
    double xabs;
    double yabs;
    double v;

    xabs = fabs(z.x);
    yabs = fabs(z.y);
    w = xabs>yabs ? xabs : yabs;
    v = xabs<yabs ? xabs : yabs;
    if( v==0 )
        return w;
    else
    {
        double t = v/w;
        return w*sqrt(1+t*t);
    }
}

ae_bool ae_c_eq(ae_complex lhs,   ae_complex rhs)
{
    volatile double x1 = lhs.x;
    volatile double x2 = rhs.x;
    volatile double y1 = lhs.y;
    volatile double y2 = rhs.y;
    return x1==x2 && y1==y2;
}

ae_bool ae_c_neq(ae_complex lhs,  ae_complex rhs)
{
    volatile double x1 = lhs.x;
    volatile double x2 = rhs.x;
    volatile double y1 = lhs.y;
    volatile double y2 = rhs.y;
    return x1!=x2 || y1!=y2;
}

ae_complex ae_c_add(ae_complex lhs,  ae_complex rhs)
{
    ae_complex result;
    result.x = lhs.x+rhs.x;
    result.y = lhs.y+rhs.y;
    return result;
}

ae_complex ae_c_mul(ae_complex lhs,  ae_complex rhs)
{
    ae_complex result;
    result.x = lhs.x*rhs.x-lhs.y*rhs.y;
    result.y = lhs.x*rhs.y+lhs.y*rhs.x;
    return result;
}

ae_complex ae_c_sub(ae_complex lhs,   ae_complex rhs)
{
    ae_complex result;
    result.x = lhs.x-rhs.x;
    result.y = lhs.y-rhs.y;
    return result;
}

ae_complex ae_c_div(ae_complex lhs,   ae_complex rhs)
{
    ae_complex result;
    double e;
    double f;
    if( fabs(rhs.y)<fabs(rhs.x) )
    {
        e = rhs.y/rhs.x;
        f = rhs.x+rhs.y*e;
        result.x = (lhs.x+lhs.y*e)/f;
        result.y = (lhs.y-lhs.x*e)/f;
    }
    else
    {
        e = rhs.x/rhs.y;
        f = rhs.y+rhs.x*e;
        result.x = (lhs.y+lhs.x*e)/f;
        result.y = (-lhs.x+lhs.y*e)/f;
    }
    return result;
}

ae_bool ae_c_eq_d(ae_complex lhs,  double rhs)
{
    volatile double x1 = lhs.x;
    volatile double x2 = rhs;
    volatile double y1 = lhs.y;
    volatile double y2 = 0;
    return x1==x2 && y1==y2;
}

ae_bool ae_c_neq_d(ae_complex lhs, double rhs)
{
    volatile double x1 = lhs.x;
    volatile double x2 = rhs;
    volatile double y1 = lhs.y;
    volatile double y2 = 0;
    return x1!=x2 || y1!=y2;
}

ae_complex ae_c_add_d(ae_complex lhs, double rhs)
{
    ae_complex result;
    result.x = lhs.x+rhs;
    result.y = lhs.y;
    return result;
}

ae_complex ae_c_mul_d(ae_complex lhs, double rhs)
{
    ae_complex result;
    result.x = lhs.x*rhs;
    result.y = lhs.y*rhs;
    return result;
}

ae_complex ae_c_sub_d(ae_complex lhs, double rhs)
{
    ae_complex result;
    result.x = lhs.x-rhs;
    result.y = lhs.y;
    return result;
}

ae_complex ae_c_d_sub(double lhs,     ae_complex rhs)
{
    ae_complex result;
    result.x = lhs-rhs.x;
    result.y = -rhs.y;
    return result;
}

ae_complex ae_c_div_d(ae_complex lhs, double rhs)
{
    ae_complex result;
    result.x = lhs.x/rhs;
    result.y = lhs.y/rhs;
    return result;
}

ae_complex ae_c_d_div(double lhs,   ae_complex rhs)
{
    ae_complex result;
    double e;
    double f;
    if( fabs(rhs.y)<fabs(rhs.x) )
    {
        e = rhs.y/rhs.x;
        f = rhs.x+rhs.y*e;
        result.x = lhs/f;
        result.y = -lhs*e/f;
    }
    else
    {
        e = rhs.x/rhs.y;
        f = rhs.y+rhs.x*e;
        result.x = lhs*e/f;
        result.y = -lhs/f;
    }
    return result;
}


/************************************************************************
Complex BLAS operations
************************************************************************/
ae_complex ae_v_cdotproduct(const ae_complex *v0, ae_int_t stride0, const char *conj0, const ae_complex *v1, ae_int_t stride1, const char *conj1, ae_int_t n)
{
    double rx = 0, ry = 0; 
    ae_int_t i;
    ae_bool bconj0 = !((conj0[0]=='N') || (conj0[0]=='n'));
    ae_bool bconj1 = !((conj1[0]=='N') || (conj1[0]=='n'));
    ae_complex result;
    if( bconj0 && bconj1 )
    {
        double v0x, v0y, v1x, v1y;
        for(i=0; i<n; i++, v0+=stride0, v1+=stride1)
        {
            v0x = v0->x;
            v0y = -v0->y;
            v1x = v1->x;
            v1y = -v1->y;
            rx += v0x*v1x-v0y*v1y;
            ry += v0x*v1y+v0y*v1x;
        }
    }
    if( !bconj0 && bconj1 )
    {
        double v0x, v0y, v1x, v1y;
        for(i=0; i<n; i++, v0+=stride0, v1+=stride1)
        {
            v0x = v0->x;
            v0y = v0->y;
            v1x = v1->x;
            v1y = -v1->y;
            rx += v0x*v1x-v0y*v1y;
            ry += v0x*v1y+v0y*v1x;
        }
    }
    if( bconj0 && !bconj1 )
    {
        double v0x, v0y, v1x, v1y;
        for(i=0; i<n; i++, v0+=stride0, v1+=stride1)
        {
            v0x = v0->x;
            v0y = -v0->y;
            v1x = v1->x;
            v1y = v1->y;
            rx += v0x*v1x-v0y*v1y;
            ry += v0x*v1y+v0y*v1x;
        }
    }
    if( !bconj0 && !bconj1 )
    {
        double v0x, v0y, v1x, v1y;
        for(i=0; i<n; i++, v0+=stride0, v1+=stride1)
        {
            v0x = v0->x;
            v0y = v0->y;
            v1x = v1->x;
            v1y = v1->y;
            rx += v0x*v1x-v0y*v1y;
            ry += v0x*v1y+v0y*v1x;
        }
    }
    result.x = rx;
    result.y = ry;
    return result;
}

void ae_v_cmove(ae_complex *vdst, ae_int_t stride_dst, const ae_complex* vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n)
{
    ae_bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x =  vsrc->x;
                vdst->y = -vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
                *vdst = *vsrc;
        }
    }
    else
    {
        /*
         * optimized case
         */
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x =  vsrc->x;
                vdst->y = -vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
                *vdst = *vsrc;
        }
    }
}

void ae_v_cmoveneg(ae_complex *vdst, ae_int_t stride_dst, const ae_complex* vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n)
{
    ae_bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x = -vsrc->x;
                vdst->y =  vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x = -vsrc->x;
                vdst->y = -vsrc->y;
            }
        }
    }
    else
    {
        /*
         * optimized case
         */
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x = -vsrc->x;
                vdst->y =  vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x = -vsrc->x;
                vdst->y = -vsrc->y;
            }
        }
    }
}

void ae_v_cmoved(ae_complex *vdst, ae_int_t stride_dst, const ae_complex* vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n, double alpha)
{
    ae_bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x =  alpha*vsrc->x;
                vdst->y = -alpha*vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x = alpha*vsrc->x;
                vdst->y = alpha*vsrc->y;
            }
        }
    }
    else
    {
        /*
         * optimized case
         */
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x =  alpha*vsrc->x;
                vdst->y = -alpha*vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x = alpha*vsrc->x;
                vdst->y = alpha*vsrc->y;
            }
        }
    }
}

void ae_v_cmovec(ae_complex *vdst, ae_int_t stride_dst, const ae_complex* vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n, ae_complex alpha)
{
    ae_bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        if( bconj )
        {
            double ax = alpha.x, ay = alpha.y;
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x =  ax*vsrc->x+ay*vsrc->y;
                vdst->y = -ax*vsrc->y+ay*vsrc->x;
            }
        }
        else
        {
            double ax = alpha.x, ay = alpha.y;
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x = ax*vsrc->x-ay*vsrc->y;
                vdst->y = ax*vsrc->y+ay*vsrc->x;
            }
        }
    }
    else
    {
        /*
         * highly optimized case
         */
        if( bconj )
        {
            double ax = alpha.x, ay = alpha.y;
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x =  ax*vsrc->x+ay*vsrc->y;
                vdst->y = -ax*vsrc->y+ay*vsrc->x;
            }
        }
        else
        {
            double ax = alpha.x, ay = alpha.y;
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x = ax*vsrc->x-ay*vsrc->y;
                vdst->y = ax*vsrc->y+ay*vsrc->x;
            }
        }
    }
}

void ae_v_cadd(ae_complex *vdst,     ae_int_t stride_dst, const ae_complex *vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n)
{
    ae_bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x += vsrc->x;
                vdst->y -= vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x += vsrc->x;
                vdst->y += vsrc->y;
            }
        }
    }
    else
    {
        /*
         * optimized case
         */
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x += vsrc->x;
                vdst->y -= vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x += vsrc->x;
                vdst->y += vsrc->y;
            }
        }
    }
}

void ae_v_caddd(ae_complex *vdst,    ae_int_t stride_dst, const ae_complex *vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n, double alpha)
{
    ae_bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x += alpha*vsrc->x;
                vdst->y -= alpha*vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x += alpha*vsrc->x;
                vdst->y += alpha*vsrc->y;
            }
        }
    }
    else
    {
        /*
         * optimized case
         */
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x += alpha*vsrc->x;
                vdst->y -= alpha*vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x += alpha*vsrc->x;
                vdst->y += alpha*vsrc->y;
            }
        }
    }
}

void ae_v_caddc(ae_complex *vdst,    ae_int_t stride_dst, const ae_complex *vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n, ae_complex alpha)
{
    ae_bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        double ax = alpha.x, ay = alpha.y;
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x += ax*vsrc->x+ay*vsrc->y;
                vdst->y -= ax*vsrc->y-ay*vsrc->x;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x += ax*vsrc->x-ay*vsrc->y;
                vdst->y += ax*vsrc->y+ay*vsrc->x;
            }
        }
    }
    else
    {
        /*
         * highly optimized case
         */
        double ax = alpha.x, ay = alpha.y;
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x += ax*vsrc->x+ay*vsrc->y;
                vdst->y -= ax*vsrc->y-ay*vsrc->x;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x += ax*vsrc->x-ay*vsrc->y;
                vdst->y += ax*vsrc->y+ay*vsrc->x;
            }
        }
    }
}

void ae_v_csub(ae_complex *vdst,     ae_int_t stride_dst, const ae_complex *vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n)
{
    ae_bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x -= vsrc->x;
                vdst->y += vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x -= vsrc->x;
                vdst->y -= vsrc->y;
            }
        }
    }
    else
    {
        /*
         * highly optimized case
         */
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x -= vsrc->x;
                vdst->y += vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x -= vsrc->x;
                vdst->y -= vsrc->y;
            }
        }
    }
}

void ae_v_csubd(ae_complex *vdst, ae_int_t stride_dst, const ae_complex *vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n, double alpha)
{
    ae_v_caddd(vdst, stride_dst, vsrc, stride_src, conj_src, n, -alpha);
}

void ae_v_csubc(ae_complex *vdst, ae_int_t stride_dst, const ae_complex *vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n, ae_complex alpha)
{
    alpha.x = -alpha.x;
    alpha.y = -alpha.y;
    ae_v_caddc(vdst, stride_dst, vsrc, stride_src, conj_src, n, alpha);
}

void ae_v_cmuld(ae_complex *vdst, ae_int_t stride_dst, ae_int_t n, double alpha)
{
    ae_int_t i;
    if( stride_dst!=1 )
    {
        /*
         * general unoptimized case
         */
        for(i=0; i<n; i++, vdst+=stride_dst)
        {
            vdst->x *= alpha;
            vdst->y *= alpha;
        }
    }
    else
    {
        /*
         * optimized case
         */
        for(i=0; i<n; i++, vdst++)
        {
            vdst->x *= alpha;
            vdst->y *= alpha;
        }
    }
}

void ae_v_cmulc(ae_complex *vdst, ae_int_t stride_dst, ae_int_t n, ae_complex alpha)
{
    ae_int_t i;
    if( stride_dst!=1 )
    {
        /*
         * general unoptimized case
         */
        double ax = alpha.x, ay = alpha.y;
        for(i=0; i<n; i++, vdst+=stride_dst)
        {
            double  dstx = vdst->x, dsty = vdst->y;
            vdst->x = ax*dstx-ay*dsty;
            vdst->y = ax*dsty+ay*dstx;
        }
    }
    else
    {
        /*
         * highly optimized case
         */
        double ax = alpha.x, ay = alpha.y;
        for(i=0; i<n; i++, vdst++)
        {
            double  dstx = vdst->x, dsty = vdst->y;
            vdst->x = ax*dstx-ay*dsty;
            vdst->y = ax*dsty+ay*dstx;
        }
    }
}

/************************************************************************
Real BLAS operations
************************************************************************/
double ae_v_dotproduct(const double *v0, ae_int_t stride0, const double *v1, ae_int_t stride1, ae_int_t n)
{
    double result = 0;
    ae_int_t i;
    if( stride0!=1 || stride1!=1 )
    {
        /*
         * slow general code
         */
        for(i=0; i<n; i++, v0+=stride0, v1+=stride1)
            result += (*v0)*(*v1);
    }
    else
    {
        /*
         * optimized code for stride=1
         */
        ae_int_t n4 = n/4;
        ae_int_t nleft = n%4;
        for(i=0; i<n4; i++, v0+=4, v1+=4)
            result += v0[0]*v1[0]+v0[1]*v1[1]+v0[2]*v1[2]+v0[3]*v1[3];
        for(i=0; i<nleft; i++, v0++, v1++)
            result += v0[0]*v1[0];
    }
    return result;
}

void ae_v_move(double *vdst,  ae_int_t stride_dst, const double* vsrc,  ae_int_t stride_src, ae_int_t n)
{
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            *vdst = *vsrc;
    }
    else
    {
        /*
         * optimized case
         */
        ae_int_t n2 = n/2;
        for(i=0; i<n2; i++, vdst+=2, vsrc+=2)
        {
            vdst[0] = vsrc[0];
            vdst[1] = vsrc[1];
        }
        if( n%2!=0 )
            vdst[0] = vsrc[0];
    }
}

void ae_v_moveneg(double *vdst,  ae_int_t stride_dst, const double* vsrc,  ae_int_t stride_src, ae_int_t n)
{
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            *vdst = -*vsrc;
    }
    else
    {
        /*
         * optimized case
         */
        ae_int_t n2 = n/2;
        for(i=0; i<n2; i++, vdst+=2, vsrc+=2)
        {
            vdst[0] = -vsrc[0];
            vdst[1] = -vsrc[1];
        }
        if( n%2!=0 )
            vdst[0] = -vsrc[0];
    }
}

void ae_v_moved(double *vdst,  ae_int_t stride_dst, const double* vsrc,  ae_int_t stride_src, ae_int_t n, double alpha)
{
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            *vdst = alpha*(*vsrc);
    }
    else
    {
        /*
         * optimized case
         */
        ae_int_t n2 = n/2;
        for(i=0; i<n2; i++, vdst+=2, vsrc+=2)
        {
            vdst[0] = alpha*vsrc[0];
            vdst[1] = alpha*vsrc[1];
        }
        if( n%2!=0 )
            vdst[0] = alpha*vsrc[0];
    }
}

void ae_v_add(double *vdst,     ae_int_t stride_dst, const double *vsrc,  ae_int_t stride_src, ae_int_t n)
{
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            *vdst += *vsrc;
    }
    else
    {
        /*
         * optimized case
         */
        ae_int_t n2 = n/2;
        for(i=0; i<n2; i++, vdst+=2, vsrc+=2)
        {
            vdst[0] += vsrc[0];
            vdst[1] += vsrc[1];
        }
        if( n%2!=0 )
            vdst[0] += vsrc[0];
    }
}

void ae_v_addd(double *vdst,    ae_int_t stride_dst, const double *vsrc,  ae_int_t stride_src, ae_int_t n, double alpha)
{
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            *vdst += alpha*(*vsrc);
    }
    else
    {
        /*
         * optimized case
         */
        ae_int_t n2 = n/2;
        for(i=0; i<n2; i++, vdst+=2, vsrc+=2)
        {
            vdst[0] += alpha*vsrc[0];
            vdst[1] += alpha*vsrc[1];
        }
        if( n%2!=0 )
            vdst[0] += alpha*vsrc[0];
    }
}

void ae_v_sub(double *vdst,     ae_int_t stride_dst, const double *vsrc,  ae_int_t stride_src, ae_int_t n)
{
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        /*
         * general unoptimized case
         */
        for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            *vdst -= *vsrc;
    }
    else
    {
        /*
         * highly optimized case
         */
        ae_int_t n2 = n/2;
        for(i=0; i<n2; i++, vdst+=2, vsrc+=2)
        {
            vdst[0] -= vsrc[0];
            vdst[1] -= vsrc[1];
        }
        if( n%2!=0 )
            vdst[0] -= vsrc[0];
    }
}

void ae_v_subd(double *vdst,  ae_int_t stride_dst, const double *vsrc,  ae_int_t stride_src, ae_int_t n, double alpha)
{
    ae_v_addd(vdst, stride_dst, vsrc, stride_src, n, -alpha);
}

void ae_v_muld(double *vdst,  ae_int_t stride_dst, ae_int_t n, double alpha)
{
    ae_int_t i;
    if( stride_dst!=1 )
    {
        /*
         * general unoptimized case
         */
        for(i=0; i<n; i++, vdst+=stride_dst)
            *vdst *= alpha;
    }
    else
    {
        /*
         * highly optimized case
         */
        for(i=0; i<n; i++, vdst++)
            *vdst *= alpha;
    }
}

/************************************************************************
Other functions
************************************************************************/
ae_int_t ae_v_len(ae_int_t a, ae_int_t b)
{
    return b-a+1;
}

/************************************************************************
RComm functions
************************************************************************/
ae_bool _rcommstate_init(rcommstate* p, ae_state *_state, ae_bool make_automatic)
{
    if( !ae_vector_init(&p->ba, 0, DT_BOOL,    _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init(&p->ia, 0, DT_INT,     _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init(&p->ra, 0, DT_REAL,    _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init(&p->ca, 0, DT_COMPLEX, _state, make_automatic) )
        return ae_false;
    return ae_true;
}

ae_bool _rcommstate_init_copy(rcommstate* dst, rcommstate* src, ae_state *_state, ae_bool make_automatic)
{
    if( !ae_vector_init_copy(&dst->ba, &src->ba, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init_copy(&dst->ia, &src->ia, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init_copy(&dst->ra, &src->ra, _state, make_automatic) )
        return ae_false;
    if( !ae_vector_init_copy(&dst->ca, &src->ca, _state, make_automatic) )
        return ae_false;
    dst->stage = src->stage;
    return ae_true;
}

void _rcommstate_clear(rcommstate* p)
{
    ae_vector_clear(&p->ba);
    ae_vector_clear(&p->ia);
    ae_vector_clear(&p->ra);
    ae_vector_clear(&p->ca);
}

void _rcommstate_destroy(rcommstate* p)
{
    _rcommstate_clear(p);
}

#ifdef AE_DEBUG4WINDOWS
int _tickcount()
{
    return GetTickCount();
}
#endif

#ifdef AE_DEBUG4POSIX
#include <sys/time.h>
int _tickcount()
{
    struct timeval now;
    ae_int64_t r, v;
    gettimeofday(&now, NULL);
    v = now.tv_sec;
    r = v*1000;
    v = now.tv_usec/1000;
    r = r+v;
    return r;
    /*struct timespec now;
    if (clock_gettime(CLOCK_MONOTONIC, &now) )
        return 0;
    return now.tv_sec * 1000.0 + now.tv_nsec / 1000000.0;*/
}
#endif


}

/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS C++ RELATED FUNCTIONALITY
//
/////////////////////////////////////////////////////////////////////////
/********************************************************************
Internal forwards
********************************************************************/
namespace alglib
{
    double get_aenv_nan();
    double get_aenv_posinf();
    double get_aenv_neginf();
    ae_int_t my_stricmp(const char *s1, const char *s2);
    char* filter_spaces(const char *s);
    void str_vector_create(const char *src, bool match_head_only, std::vector<const char*> *p_vec);
    void str_matrix_create(const char *src, std::vector< std::vector<const char*> > *p_mat);
    
    ae_bool parse_bool_delim(const char *s, const char *delim);
    ae_int_t parse_int_delim(const char *s, const char *delim);
    bool _parse_real_delim(const char *s, const char *delim, double *result, const char **new_s);
    double parse_real_delim(const char *s, const char *delim);
    alglib::complex parse_complex_delim(const char *s, const char *delim);

    std::string arraytostring(const bool *ptr, ae_int_t n);
    std::string arraytostring(const ae_int_t *ptr, ae_int_t n);
    std::string arraytostring(const double *ptr, ae_int_t n, int dps);
    std::string arraytostring(const alglib::complex *ptr, ae_int_t n, int dps);
}

/********************************************************************
Global and local constants
********************************************************************/
const double alglib::machineepsilon = 5E-16;
const double alglib::maxrealnumber  = 1E300;
const double alglib::minrealnumber  = 1E-300;
const alglib::ae_int_t alglib::endianness =  alglib_impl::ae_get_endianness();
const double alglib::fp_nan         =  alglib::get_aenv_nan();
const double alglib::fp_posinf      =  alglib::get_aenv_posinf();
const double alglib::fp_neginf      =  alglib::get_aenv_neginf();


/********************************************************************
ap_error
********************************************************************/
alglib::ap_error::ap_error()
{
}

alglib::ap_error::ap_error(const char *s)
{
    msg = s; 
}

void alglib::ap_error::make_assertion(bool bClause)
{
    if(!bClause) 
        throw ap_error(); 
}

void alglib::ap_error::make_assertion(bool bClause, const char *msg)
{ 
    if(!bClause) 
        throw ap_error(msg); 
}


/********************************************************************
Complex number with double precision.
********************************************************************/
alglib::complex::complex():x(0.0),y(0.0)
{
}

alglib::complex::complex(const double &_x):x(_x),y(0.0)
{
}

alglib::complex::complex(const double &_x, const double &_y):x(_x),y(_y)
{
}

alglib::complex::complex(const alglib::complex &z):x(z.x),y(z.y)
{
}

alglib::complex& alglib::complex::operator= (const double& v)
{
    x = v; 
    y = 0.0; 
    return *this; 
}

alglib::complex& alglib::complex::operator+=(const double& v)
{
    x += v;
    return *this; 
}

alglib::complex& alglib::complex::operator-=(const double& v)
{
    x -= v;
    return *this;
}

alglib::complex& alglib::complex::operator*=(const double& v)
{
    x *= v;
    y *= v;
    return *this; 
}

alglib::complex& alglib::complex::operator/=(const double& v)
{
    x /= v;
    y /= v;
    return *this;
}

alglib::complex& alglib::complex::operator= (const alglib::complex& z)
{
    x = z.x;
    y = z.y;
    return *this;
}

alglib::complex& alglib::complex::operator+=(const alglib::complex& z)
{
    x += z.x;
    y += z.y;
    return *this;
}

alglib::complex& alglib::complex::operator-=(const alglib::complex& z)
{
    x -= z.x;
    y -= z.y;
    return *this;
}

alglib::complex& alglib::complex::operator*=(const alglib::complex& z)
{
    double t = x*z.x-y*z.y;
    y = x*z.y+y*z.x;
    x = t; 
    return *this;
}

alglib::complex& alglib::complex::operator/=(const alglib::complex& z)
{
    alglib::complex result;
    double e;
    double f;
    if( fabs(z.y)<fabs(z.x) )
    {
        e = z.y/z.x;
        f = z.x+z.y*e;
        result.x = (x+y*e)/f;
        result.y = (y-x*e)/f;
    }
    else
    {
        e = z.x/z.y;
        f = z.y+z.x*e;
        result.x = (y+x*e)/f;
        result.y = (-x+y*e)/f;
    }
    *this = result;
    return *this;
}

alglib_impl::ae_complex* alglib::complex::c_ptr()
{
    return (alglib_impl::ae_complex*)this;
}

const alglib_impl::ae_complex* alglib::complex::c_ptr() const
{
    return (const alglib_impl::ae_complex*)this;
}
    
std::string alglib::complex::tostring(int _dps) const
{
    char mask[32];
    char buf_x[32];
    char buf_y[32];
    char buf_zero[32];
    int dps = _dps>=0 ? _dps : -_dps;
    if( dps<=0 || dps>=20 )
        throw ap_error("complex::tostring(): incorrect dps");

    // handle IEEE special quantities
    if( fp_isnan(x) || fp_isnan(y) )
        return "NAN";
    if( fp_isinf(x) || fp_isinf(y) )
        return "INF";

    // generate mask
    if( sprintf(mask, "%%.%d%s", dps, _dps>=0 ? "f" : "e")>=(int)sizeof(mask) )
        throw ap_error("complex::tostring(): buffer overflow");

    // print |x|, |y| and zero with same mask and compare
    if( sprintf(buf_x, mask, (double)(fabs(x)))>=(int)sizeof(buf_x) )
        throw ap_error("complex::tostring(): buffer overflow");
    if( sprintf(buf_y, mask, (double)(fabs(y)))>=(int)sizeof(buf_y) )
        throw ap_error("complex::tostring(): buffer overflow");
    if( sprintf(buf_zero, mask, (double)0)>=(int)sizeof(buf_zero) )
        throw ap_error("complex::tostring(): buffer overflow");

    // different zero/nonzero patterns
    if( strcmp(buf_x,buf_zero)!=0 && strcmp(buf_y,buf_zero)!=0 )
        return std::string(x>0 ? "" : "-")+buf_x+(y>0 ? "+" : "-")+buf_y+"i";
    if( strcmp(buf_x,buf_zero)!=0 && strcmp(buf_y,buf_zero)==0 )
        return std::string(x>0 ? "" : "-")+buf_x;
    if( strcmp(buf_x,buf_zero)==0 && strcmp(buf_y,buf_zero)!=0 )
        return std::string(y>0 ? "" : "-")+buf_y+"i";
    return std::string("0");
}

const bool alglib::operator==(const alglib::complex& lhs, const alglib::complex& rhs)
{
    volatile double x1 = lhs.x;
    volatile double x2 = rhs.x;
    volatile double y1 = lhs.y;
    volatile double y2 = rhs.y;
    return x1==x2 && y1==y2;
}

const bool alglib::operator!=(const alglib::complex& lhs, const alglib::complex& rhs)
{ return !(lhs==rhs); }

const alglib::complex alglib::operator+(const alglib::complex& lhs)
{ return lhs; }

const alglib::complex alglib::operator-(const alglib::complex& lhs)
{ return alglib::complex(-lhs.x, -lhs.y); }

const alglib::complex alglib::operator+(const alglib::complex& lhs, const alglib::complex& rhs)
{ alglib::complex r = lhs; r += rhs; return r; }

const alglib::complex alglib::operator+(const alglib::complex& lhs, const double& rhs)
{ alglib::complex r = lhs; r += rhs; return r; }

const alglib::complex alglib::operator+(const double& lhs, const alglib::complex& rhs)
{ alglib::complex r = rhs; r += lhs; return r; }

const alglib::complex alglib::operator-(const alglib::complex& lhs, const alglib::complex& rhs)
{ alglib::complex r = lhs; r -= rhs; return r; }

const alglib::complex alglib::operator-(const alglib::complex& lhs, const double& rhs)
{ alglib::complex r = lhs; r -= rhs; return r; }

const alglib::complex alglib::operator-(const double& lhs, const alglib::complex& rhs)
{ alglib::complex r = lhs; r -= rhs; return r; }

const alglib::complex alglib::operator*(const alglib::complex& lhs, const alglib::complex& rhs)
{ return alglib::complex(lhs.x*rhs.x - lhs.y*rhs.y,  lhs.x*rhs.y + lhs.y*rhs.x); }

const alglib::complex alglib::operator*(const alglib::complex& lhs, const double& rhs)
{ return alglib::complex(lhs.x*rhs,  lhs.y*rhs); }

const alglib::complex alglib::operator*(const double& lhs, const alglib::complex& rhs)
{ return alglib::complex(lhs*rhs.x,  lhs*rhs.y); }

const alglib::complex alglib::operator/(const alglib::complex& lhs, const alglib::complex& rhs)
{
    alglib::complex result;
    double e;
    double f;
    if( fabs(rhs.y)<fabs(rhs.x) )
    {
        e = rhs.y/rhs.x;
        f = rhs.x+rhs.y*e;
        result.x = (lhs.x+lhs.y*e)/f;
        result.y = (lhs.y-lhs.x*e)/f;
    }
    else
    {
        e = rhs.x/rhs.y;
        f = rhs.y+rhs.x*e;
        result.x = (lhs.y+lhs.x*e)/f;
        result.y = (-lhs.x+lhs.y*e)/f;
    }
    return result;
}

const alglib::complex alglib::operator/(const double& lhs, const alglib::complex& rhs)
{
    alglib::complex result;
    double e;
    double f;
    if( fabs(rhs.y)<fabs(rhs.x) )
    {
        e = rhs.y/rhs.x;
        f = rhs.x+rhs.y*e;
        result.x = lhs/f;
        result.y = -lhs*e/f;
    }
    else
    {
        e = rhs.x/rhs.y;
        f = rhs.y+rhs.x*e;
        result.x = lhs*e/f;
        result.y = -lhs/f;
    }
    return result;
}

const alglib::complex alglib::operator/(const alglib::complex& lhs, const double& rhs)
{ return alglib::complex(lhs.x/rhs, lhs.y/rhs); }

double alglib::abscomplex(const alglib::complex &z)
{
    double w;
    double xabs;
    double yabs;
    double v;

    xabs = fabs(z.x);
    yabs = fabs(z.y);
    w = xabs>yabs ? xabs : yabs;
    v = xabs<yabs ? xabs : yabs; 
    if( v==0 )
        return w;
    else
    {
        double t = v/w;
        return w*sqrt(1+t*t);
    }
}

alglib::complex alglib::conj(const alglib::complex &z)
{ return alglib::complex(z.x, -z.y); }

alglib::complex alglib::csqr(const alglib::complex &z)
{ return alglib::complex(z.x*z.x-z.y*z.y, 2*z.x*z.y); }

void alglib::setnworkers(alglib::ae_int_t nworkers)
{
#ifdef AE_HPC
    alglib_impl::ae_set_cores_to_use(nworkers);
#endif
}

/********************************************************************
Level 1 BLAS functions
********************************************************************/
double alglib::vdotproduct(const double *v0, ae_int_t stride0, const double *v1, ae_int_t stride1, ae_int_t n)
{
    double result = 0;
    ae_int_t i;
    if( stride0!=1 || stride1!=1 )
    {
        //
        // slow general code
        //
        for(i=0; i<n; i++, v0+=stride0, v1+=stride1)
            result += (*v0)*(*v1);
    }
    else
    {
        //
        // optimized code for stride=1
        //
        ae_int_t n4 = n/4;
        ae_int_t nleft = n%4;
        for(i=0; i<n4; i++, v0+=4, v1+=4)
            result += v0[0]*v1[0]+v0[1]*v1[1]+v0[2]*v1[2]+v0[3]*v1[3];
        for(i=0; i<nleft; i++, v0++, v1++)
            result += v0[0]*v1[0];
    }
    return result;
}

double alglib::vdotproduct(const double *v1, const double *v2, ae_int_t N)
{
    return vdotproduct(v1, 1, v2, 1, N);
}

alglib::complex alglib::vdotproduct(const alglib::complex *v0, ae_int_t stride0, const char *conj0, const alglib::complex *v1, ae_int_t stride1, const char *conj1, ae_int_t n)
{
    double rx = 0, ry = 0;
    ae_int_t i;
    bool bconj0 = !((conj0[0]=='N') || (conj0[0]=='n'));
    bool bconj1 = !((conj1[0]=='N') || (conj1[0]=='n'));
    if( bconj0 && bconj1 )
    {
        double v0x, v0y, v1x, v1y;
        for(i=0; i<n; i++, v0+=stride0, v1+=stride1)
        {
            v0x = v0->x;
            v0y = -v0->y;
            v1x = v1->x;
            v1y = -v1->y;
            rx += v0x*v1x-v0y*v1y;
            ry += v0x*v1y+v0y*v1x;
        }
    }
    if( !bconj0 && bconj1 )
    {
        double v0x, v0y, v1x, v1y;
        for(i=0; i<n; i++, v0+=stride0, v1+=stride1)
        {
            v0x = v0->x;
            v0y = v0->y;
            v1x = v1->x;
            v1y = -v1->y;
            rx += v0x*v1x-v0y*v1y;
            ry += v0x*v1y+v0y*v1x;
        }
    }
    if( bconj0 && !bconj1 )
    {
        double v0x, v0y, v1x, v1y;
        for(i=0; i<n; i++, v0+=stride0, v1+=stride1)
        {
            v0x = v0->x;
            v0y = -v0->y;
            v1x = v1->x;
            v1y = v1->y;
            rx += v0x*v1x-v0y*v1y;
            ry += v0x*v1y+v0y*v1x;
        }
    }
    if( !bconj0 && !bconj1 )
    {
        double v0x, v0y, v1x, v1y;
        for(i=0; i<n; i++, v0+=stride0, v1+=stride1)
        {
            v0x = v0->x;
            v0y = v0->y;
            v1x = v1->x;
            v1y = v1->y;
            rx += v0x*v1x-v0y*v1y;
            ry += v0x*v1y+v0y*v1x;
        }
    }
    return alglib::complex(rx,ry);
}

alglib::complex alglib::vdotproduct(const alglib::complex *v1, const alglib::complex *v2, ae_int_t N)
{
    return vdotproduct(v1, 1, "N", v2, 1, "N", N);
}

void alglib::vmove(double *vdst, ae_int_t stride_dst, const double* vsrc,  ae_int_t stride_src, ae_int_t n)
{
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            *vdst = *vsrc;
    }
    else
    {
        //
        // optimized case
        //
        ae_int_t n2 = n/2;
        for(i=0; i<n2; i++, vdst+=2, vsrc+=2)
        {
            vdst[0] = vsrc[0];
            vdst[1] = vsrc[1];
        }
        if( n%2!=0 )
            vdst[0] = vsrc[0];
    }
}

void alglib::vmove(double *vdst, const double* vsrc, ae_int_t N)
{
    vmove(vdst, 1, vsrc, 1, N);
}

void alglib::vmove(alglib::complex *vdst, ae_int_t stride_dst, const alglib::complex* vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n)
{
    bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x =  vsrc->x;
                vdst->y = -vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
                *vdst = *vsrc;
        }
    }
    else
    {
        //
        // optimized case
        //
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x =  vsrc->x;
                vdst->y = -vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
                *vdst = *vsrc;
        }
    }
}

void alglib::vmove(alglib::complex *vdst, const alglib::complex* vsrc, ae_int_t N)
{
    vmove(vdst, 1, vsrc, 1, "N", N);
}

void alglib::vmoveneg(double *vdst,  ae_int_t stride_dst, const double* vsrc,  ae_int_t stride_src, ae_int_t n)
{
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            *vdst = -*vsrc;
    }
    else
    {
        //
        // optimized case
        //
        ae_int_t n2 = n/2;
        for(i=0; i<n2; i++, vdst+=2, vsrc+=2)
        {
            vdst[0] = -vsrc[0];
            vdst[1] = -vsrc[1];
        }
        if( n%2!=0 )
            vdst[0] = -vsrc[0];
    }
}

void alglib::vmoveneg(double *vdst, const double *vsrc, ae_int_t N)
{
    vmoveneg(vdst, 1, vsrc, 1, N);
}

void alglib::vmoveneg(alglib::complex *vdst, ae_int_t stride_dst, const alglib::complex* vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n)
{
    bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x = -vsrc->x;
                vdst->y =  vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x = -vsrc->x;
                vdst->y = -vsrc->y;
            }
        }
    }
    else
    {
        //
        // optimized case
        //
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x = -vsrc->x;
                vdst->y =  vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x = -vsrc->x;
                vdst->y = -vsrc->y;
            }
        }
    }
}

void alglib::vmoveneg(alglib::complex *vdst, const alglib::complex *vsrc, ae_int_t N)
{
    vmoveneg(vdst, 1, vsrc, 1, "N", N);
}

void alglib::vmove(double *vdst,  ae_int_t stride_dst, const double* vsrc,  ae_int_t stride_src, ae_int_t n, double alpha)
{
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            *vdst = alpha*(*vsrc);
    }
    else
    {
        //
        // optimized case
        //
        ae_int_t n2 = n/2;
        for(i=0; i<n2; i++, vdst+=2, vsrc+=2)
        {
            vdst[0] = alpha*vsrc[0];
            vdst[1] = alpha*vsrc[1];
        }
        if( n%2!=0 )
            vdst[0] = alpha*vsrc[0];
    }
}

void alglib::vmove(double *vdst, const double *vsrc, ae_int_t N, double alpha)
{
    vmove(vdst, 1, vsrc, 1, N, alpha);
}

void alglib::vmove(alglib::complex *vdst, ae_int_t stride_dst, const alglib::complex* vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n, double alpha)
{
    bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x =  alpha*vsrc->x;
                vdst->y = -alpha*vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x = alpha*vsrc->x;
                vdst->y = alpha*vsrc->y;
            }
        }
    }
    else
    {
        //
        // optimized case
        //
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x =  alpha*vsrc->x;
                vdst->y = -alpha*vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x = alpha*vsrc->x;
                vdst->y = alpha*vsrc->y;
            }
        }
    }
}

void alglib::vmove(alglib::complex *vdst, const alglib::complex *vsrc, ae_int_t N, double alpha)
{
    vmove(vdst, 1, vsrc, 1, "N", N, alpha);
}

void alglib::vmove(alglib::complex *vdst, ae_int_t stride_dst, const alglib::complex* vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n, alglib::complex alpha)
{
    bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        if( bconj )
        {
            double ax = alpha.x, ay = alpha.y;
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x =  ax*vsrc->x+ay*vsrc->y;
                vdst->y = -ax*vsrc->y+ay*vsrc->x;
            }
        }
        else
        {
            double ax = alpha.x, ay = alpha.y;
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x = ax*vsrc->x-ay*vsrc->y;
                vdst->y = ax*vsrc->y+ay*vsrc->x;
            }
        }
    }
    else
    {
        //
        // optimized case
        //
        if( bconj )
        {
            double ax = alpha.x, ay = alpha.y;
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x =  ax*vsrc->x+ay*vsrc->y;
                vdst->y = -ax*vsrc->y+ay*vsrc->x;
            }
        }
        else
        {
            double ax = alpha.x, ay = alpha.y;
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x = ax*vsrc->x-ay*vsrc->y;
                vdst->y = ax*vsrc->y+ay*vsrc->x;
            }
        }
    }
}

void alglib::vmove(alglib::complex *vdst, const alglib::complex *vsrc, ae_int_t N, alglib::complex alpha)
{
    vmove(vdst, 1, vsrc, 1, "N", N, alpha);
}

void alglib::vadd(double *vdst,  ae_int_t stride_dst, const double *vsrc,  ae_int_t stride_src, ae_int_t n)
{
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            *vdst += *vsrc;
    }
    else
    {
        //
        // optimized case
        //
        ae_int_t n2 = n/2;
        for(i=0; i<n2; i++, vdst+=2, vsrc+=2)
        {
            vdst[0] += vsrc[0];
            vdst[1] += vsrc[1];
        }
        if( n%2!=0 )
            vdst[0] += vsrc[0];
    }
}

void alglib::vadd(double *vdst, const double *vsrc, ae_int_t N)
{
    vadd(vdst, 1, vsrc, 1, N);
}

void alglib::vadd(alglib::complex *vdst, ae_int_t stride_dst, const alglib::complex *vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n)
{
    bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x += vsrc->x;
                vdst->y -= vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x += vsrc->x;
                vdst->y += vsrc->y;
            }
        }
    }
    else
    {
        //
        // optimized case
        //
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x += vsrc->x;
                vdst->y -= vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x += vsrc->x;
                vdst->y += vsrc->y;
            }
        }
    }
}

void alglib::vadd(alglib::complex *vdst, const alglib::complex *vsrc, ae_int_t N)
{
    vadd(vdst, 1, vsrc, 1, "N", N);
}

void alglib::vadd(double *vdst,  ae_int_t stride_dst, const double *vsrc,  ae_int_t stride_src, ae_int_t n, double alpha)
{
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            *vdst += alpha*(*vsrc);
    }
    else
    {
        //
        // optimized case
        //
        ae_int_t n2 = n/2;
        for(i=0; i<n2; i++, vdst+=2, vsrc+=2)
        {
            vdst[0] += alpha*vsrc[0];
            vdst[1] += alpha*vsrc[1];
        }
        if( n%2!=0 )
            vdst[0] += alpha*vsrc[0];
    }
}

void alglib::vadd(double *vdst, const double *vsrc, ae_int_t N, double alpha)
{
    vadd(vdst, 1, vsrc, 1, N, alpha);
}

void alglib::vadd(alglib::complex *vdst, ae_int_t stride_dst, const alglib::complex *vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n, double alpha)
{
    bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x += alpha*vsrc->x;
                vdst->y -= alpha*vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x += alpha*vsrc->x;
                vdst->y += alpha*vsrc->y;
            }
        }
    }
    else
    {
        //
        // optimized case
        //
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x += alpha*vsrc->x;
                vdst->y -= alpha*vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x += alpha*vsrc->x;
                vdst->y += alpha*vsrc->y;
            }
        }
    }
}

void alglib::vadd(alglib::complex *vdst, const alglib::complex *vsrc, ae_int_t N, double alpha)
{
    vadd(vdst, 1, vsrc, 1, "N", N, alpha);
}

void alglib::vadd(alglib::complex *vdst, ae_int_t stride_dst, const alglib::complex *vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n, alglib::complex alpha)
{
    bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        double ax = alpha.x, ay = alpha.y;
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x += ax*vsrc->x+ay*vsrc->y;
                vdst->y -= ax*vsrc->y-ay*vsrc->x;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x += ax*vsrc->x-ay*vsrc->y;
                vdst->y += ax*vsrc->y+ay*vsrc->x;
            }
        }
    }
    else
    {
        //
        // optimized case
        //
        double ax = alpha.x, ay = alpha.y;
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x += ax*vsrc->x+ay*vsrc->y;
                vdst->y -= ax*vsrc->y-ay*vsrc->x;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x += ax*vsrc->x-ay*vsrc->y;
                vdst->y += ax*vsrc->y+ay*vsrc->x;
            }
        }
    }
}

void alglib::vadd(alglib::complex *vdst, const alglib::complex *vsrc, ae_int_t N, alglib::complex alpha)
{
    vadd(vdst, 1, vsrc, 1, "N", N, alpha);
}

void alglib::vsub(double *vdst,  ae_int_t stride_dst, const double *vsrc,  ae_int_t stride_src, ae_int_t n)
{
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            *vdst -= *vsrc;
    }
    else
    {
        //
        // optimized case
        //
        ae_int_t n2 = n/2;
        for(i=0; i<n2; i++, vdst+=2, vsrc+=2)
        {
            vdst[0] -= vsrc[0];
            vdst[1] -= vsrc[1];
        }
        if( n%2!=0 )
            vdst[0] -= vsrc[0];
    }
}

void alglib::vsub(double *vdst, const double *vsrc, ae_int_t N)
{
    vsub(vdst, 1, vsrc, 1, N);
}

void alglib::vsub(alglib::complex *vdst, ae_int_t stride_dst, const alglib::complex *vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n)
{
    bool bconj = !((conj_src[0]=='N') || (conj_src[0]=='n'));
    ae_int_t i;
    if( stride_dst!=1 || stride_src!=1 )
    {
        //
        // general unoptimized case
        //
        if( bconj )
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x -= vsrc->x;
                vdst->y += vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst+=stride_dst, vsrc+=stride_src)
            {
                vdst->x -= vsrc->x;
                vdst->y -= vsrc->y;
            }
        }
    }
    else
    {
        //
        // optimized case
        //
        if( bconj )
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x -= vsrc->x;
                vdst->y += vsrc->y;
            }
        }
        else
        {
            for(i=0; i<n; i++, vdst++, vsrc++)
            {
                vdst->x -= vsrc->x;
                vdst->y -= vsrc->y;
            }
        }
    }
}

void alglib::vsub(alglib::complex *vdst, const alglib::complex *vsrc, ae_int_t N)
{
    vsub(vdst, 1, vsrc, 1, "N", N);
}

void alglib::vsub(double *vdst,  ae_int_t stride_dst, const double *vsrc,  ae_int_t stride_src, ae_int_t n, double alpha)
{
    vadd(vdst, stride_dst, vsrc, stride_src, n, -alpha);
}

void alglib::vsub(double *vdst, const double *vsrc, ae_int_t N, double alpha)
{
    vadd(vdst, 1, vsrc, 1, N, -alpha);
}

void alglib::vsub(alglib::complex *vdst, ae_int_t stride_dst, const alglib::complex *vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n, double alpha)
{
    vadd(vdst, stride_dst, vsrc, stride_src, conj_src, n, -alpha);
}

void alglib::vsub(alglib::complex *vdst, const alglib::complex *vsrc, ae_int_t n, double alpha)
{
    vadd(vdst, 1, vsrc, 1, "N", n, -alpha);
}

void alglib::vsub(alglib::complex *vdst, ae_int_t stride_dst, const alglib::complex *vsrc, ae_int_t stride_src, const char *conj_src, ae_int_t n, alglib::complex alpha)
{
    vadd(vdst, stride_dst, vsrc, stride_src, conj_src, n, -alpha);
}

void alglib::vsub(alglib::complex *vdst, const alglib::complex *vsrc, ae_int_t n, alglib::complex alpha)
{
    vadd(vdst, 1, vsrc, 1, "N", n, -alpha);
}
void alglib::vmul(double *vdst,  ae_int_t stride_dst, ae_int_t n, double alpha)
{
    ae_int_t i;
    if( stride_dst!=1 )
    {
        //
        // general unoptimized case
        //
        for(i=0; i<n; i++, vdst+=stride_dst)
            *vdst *= alpha;
    }
    else
    {
        //
        // optimized case
        //
        for(i=0; i<n; i++, vdst++)
            *vdst *= alpha;
    }
}

void alglib::vmul(double *vdst, ae_int_t N, double alpha)
{
    vmul(vdst, 1, N, alpha);
}

void alglib::vmul(alglib::complex *vdst, ae_int_t stride_dst, ae_int_t n, double alpha)
{
    ae_int_t i;
    if( stride_dst!=1 )
    {
        //
        // general unoptimized case
        //
        for(i=0; i<n; i++, vdst+=stride_dst)
        {
            vdst->x *= alpha;
            vdst->y *= alpha;
        }
    }
    else
    {
        //
        // optimized case
        //
        for(i=0; i<n; i++, vdst++)
        {
            vdst->x *= alpha;
            vdst->y *= alpha;
        }
    }
}

void alglib::vmul(alglib::complex *vdst, ae_int_t N, double alpha)
{
    vmul(vdst, 1, N, alpha);
}

void alglib::vmul(alglib::complex *vdst, ae_int_t stride_dst, ae_int_t n, alglib::complex alpha)
{
    ae_int_t i;
    if( stride_dst!=1 )
    {
        //
        // general unoptimized case
        //
        double ax = alpha.x, ay = alpha.y;
        for(i=0; i<n; i++, vdst+=stride_dst)
        {
            double  dstx = vdst->x, dsty = vdst->y;
            vdst->x = ax*dstx-ay*dsty;
            vdst->y = ax*dsty+ay*dstx;
        }
    }
    else
    {
        //
        // optimized case
        //
        double ax = alpha.x, ay = alpha.y;
        for(i=0; i<n; i++, vdst++)
        {
            double  dstx = vdst->x, dsty = vdst->y;
            vdst->x = ax*dstx-ay*dsty;
            vdst->y = ax*dsty+ay*dstx;
        }
    }
}

void alglib::vmul(alglib::complex *vdst, ae_int_t N, alglib::complex alpha)
{
    vmul(vdst, 1, N, alpha);
}


/********************************************************************
Matrices and vectors
********************************************************************/
alglib::ae_vector_wrapper::ae_vector_wrapper()
{
    p_vec = NULL;
}

alglib::ae_vector_wrapper::~ae_vector_wrapper()
{
    if( p_vec==&vec )
        ae_vector_clear(p_vec);
}

void alglib::ae_vector_wrapper::setlength(ae_int_t iLen)
{
    if( p_vec==NULL )
        throw alglib::ap_error("ALGLIB: setlength() error, p_vec==NULL (array was not correctly initialized)");
    if( p_vec!=&vec )
        throw alglib::ap_error("ALGLIB: setlength() error, p_vec!=&vec (attempt to resize frozen array)");
    if( !ae_vector_set_length(p_vec, iLen, NULL) )
        throw alglib::ap_error("ALGLIB: malloc error");
}

alglib::ae_int_t alglib::ae_vector_wrapper::length() const
{
    if( p_vec==NULL )
        return 0;
    return p_vec->cnt;
}

void alglib::ae_vector_wrapper::attach_to(alglib_impl::ae_vector *ptr)
{
    if( ptr==&vec )
        throw alglib::ap_error("ALGLIB: attempt to attach vector to itself");
    if( p_vec==&vec )
        ae_vector_clear(p_vec);
    p_vec = ptr;
}

void alglib::ae_vector_wrapper::allocate_own(ae_int_t size, alglib_impl::ae_datatype datatype)
{
    if( p_vec==&vec )
        ae_vector_clear(p_vec);
    p_vec = &vec;
    if( !ae_vector_init(p_vec, size, datatype, NULL, false) )
        throw alglib::ap_error("ALGLIB: malloc error");
}

const alglib_impl::ae_vector* alglib::ae_vector_wrapper::c_ptr() const
{
    return p_vec;
}

alglib_impl::ae_vector* alglib::ae_vector_wrapper::c_ptr()
{
    return p_vec;
}

void alglib::ae_vector_wrapper::create(const alglib::ae_vector_wrapper &rhs)
{
    if( rhs.p_vec!=NULL )
    {
        p_vec = &vec;
        if( !ae_vector_init_copy(p_vec, rhs.p_vec, NULL, ae_false) )
            throw alglib::ap_error("ALGLIB: malloc error!");
    }
    else
        p_vec = NULL;
}

void alglib::ae_vector_wrapper::create(const char *s, alglib_impl::ae_datatype datatype)
{
    std::vector<const char*> svec;
    size_t i;
    char *p = filter_spaces(s);
    try
    {
        str_vector_create(p, true, &svec);
        allocate_own((ae_int_t)(svec.size()), datatype);
        for(i=0; i<svec.size(); i++)
        {
            if( datatype==alglib_impl::DT_BOOL )
                p_vec->ptr.p_bool[i]    = parse_bool_delim(svec[i],",]");
            if( datatype==alglib_impl::DT_INT )
                p_vec->ptr.p_int[i]     = parse_int_delim(svec[i],",]");
            if( datatype==alglib_impl::DT_REAL )
                p_vec->ptr.p_double[i]  = parse_real_delim(svec[i],",]");
            if( datatype==alglib_impl::DT_COMPLEX )
            {
                alglib::complex t = parse_complex_delim(svec[i],",]");
                p_vec->ptr.p_complex[i].x = t.x;
                p_vec->ptr.p_complex[i].y = t.y;
            }
        }
        alglib_impl::ae_free(p);
    }
    catch(...)
    {
        alglib_impl::ae_free(p);
        throw;
    }
}

void alglib::ae_vector_wrapper::assign(const alglib::ae_vector_wrapper &rhs)
{
    if( this==&rhs )
        return;
    if( p_vec==&vec || p_vec==NULL )
    {
        //
        // Assignment to non-proxy object
        //
        ae_vector_clear(p_vec);
        if( rhs.p_vec!=NULL )
        {
            p_vec = &vec;
            if( !ae_vector_init_copy(p_vec, rhs.p_vec, NULL, ae_false) )
                throw alglib::ap_error("ALGLIB: malloc error!");
        }
        else
            p_vec = NULL;
    }
    else
    {
        //
        // Assignment to proxy object
        //
        if( rhs.p_vec==NULL )
            throw alglib::ap_error("ALGLIB: incorrect assignment to array (sizes dont match)");
        if( rhs.p_vec->datatype!=p_vec->datatype )
            throw alglib::ap_error("ALGLIB: incorrect assignment to array (types dont match)");
        if( rhs.p_vec->cnt!=p_vec->cnt )
            throw alglib::ap_error("ALGLIB: incorrect assignment to array (sizes dont match)");
        memcpy(p_vec->ptr.p_ptr, rhs.p_vec->ptr.p_ptr, p_vec->cnt*alglib_impl::ae_sizeof(p_vec->datatype));
    }
}
    
alglib::boolean_1d_array::boolean_1d_array()  
{
    allocate_own(0, alglib_impl::DT_BOOL);
}

alglib::boolean_1d_array::boolean_1d_array(const char *s)  
{
    create(s, alglib_impl::DT_BOOL);
}

alglib::boolean_1d_array::boolean_1d_array(const alglib::boolean_1d_array &rhs)
{
    create(rhs);
}

alglib::boolean_1d_array::boolean_1d_array(alglib_impl::ae_vector *p)  
{
    p_vec = NULL;
    attach_to(p);
}

const alglib::boolean_1d_array& alglib::boolean_1d_array::operator=(const alglib::boolean_1d_array &rhs)
{
    assign(rhs);
    return *this;
}

alglib::boolean_1d_array::~boolean_1d_array() 
{
}

const ae_bool& alglib::boolean_1d_array::operator()(ae_int_t i) const
{
    return p_vec->ptr.p_bool[i];
}

ae_bool& alglib::boolean_1d_array::operator()(ae_int_t i)
{
    return p_vec->ptr.p_bool[i];
}

const ae_bool& alglib::boolean_1d_array::operator[](ae_int_t i) const
{
    return p_vec->ptr.p_bool[i];
}

ae_bool& alglib::boolean_1d_array::operator[](ae_int_t i)
{
    return p_vec->ptr.p_bool[i];
}

void alglib::boolean_1d_array::setcontent(ae_int_t iLen, const bool *pContent )
{
    ae_int_t i;
    setlength(iLen);
    for(i=0; i<iLen; i++)
        p_vec->ptr.p_bool[i] = pContent[i];
}

ae_bool* alglib::boolean_1d_array::getcontent()
{
    return p_vec->ptr.p_bool;
}

const ae_bool* alglib::boolean_1d_array::getcontent() const
{
    return p_vec->ptr.p_bool;
}

std::string alglib::boolean_1d_array::tostring() const 
{
    if( length()==0 )
        return "[]";
    return arraytostring(&(operator()(0)), length());
}

alglib::integer_1d_array::integer_1d_array()  
{
    allocate_own(0, alglib_impl::DT_INT);
}

alglib::integer_1d_array::integer_1d_array(alglib_impl::ae_vector *p)  
{
    p_vec = NULL;
    attach_to(p);
}

alglib::integer_1d_array::integer_1d_array(const char *s)  
{
    create(s, alglib_impl::DT_INT);
}

alglib::integer_1d_array::integer_1d_array(const alglib::integer_1d_array &rhs)
{
    create(rhs);
}

const alglib::integer_1d_array& alglib::integer_1d_array::operator=(const alglib::integer_1d_array &rhs)
{
    assign(rhs);
    return *this;
}

alglib::integer_1d_array::~integer_1d_array() 
{
}

const alglib::ae_int_t& alglib::integer_1d_array::operator()(ae_int_t i) const
{
    return p_vec->ptr.p_int[i];
}

alglib::ae_int_t& alglib::integer_1d_array::operator()(ae_int_t i)
{
    return p_vec->ptr.p_int[i];
}

const alglib::ae_int_t& alglib::integer_1d_array::operator[](ae_int_t i) const
{
    return p_vec->ptr.p_int[i];
}

alglib::ae_int_t& alglib::integer_1d_array::operator[](ae_int_t i)
{
    return p_vec->ptr.p_int[i];
}

void alglib::integer_1d_array::setcontent(ae_int_t iLen, const ae_int_t *pContent )
{
    ae_int_t i;
    setlength(iLen);
    for(i=0; i<iLen; i++)
        p_vec->ptr.p_int[i] = pContent[i];
}

alglib::ae_int_t* alglib::integer_1d_array::getcontent()
{
    return p_vec->ptr.p_int;
}

const alglib::ae_int_t* alglib::integer_1d_array::getcontent() const
{
    return p_vec->ptr.p_int;
}

std::string alglib::integer_1d_array::tostring() const 
{
    if( length()==0 )
        return "[]";
    return arraytostring(&operator()(0), length());
}

alglib::real_1d_array::real_1d_array()  
{
    allocate_own(0, alglib_impl::DT_REAL);
}

alglib::real_1d_array::real_1d_array(alglib_impl::ae_vector *p)  
{
    p_vec = NULL;
    attach_to(p);
}

alglib::real_1d_array::real_1d_array(const char *s)  
{
    create(s, alglib_impl::DT_REAL);
}

alglib::real_1d_array::real_1d_array(const alglib::real_1d_array &rhs)
{
    create(rhs);
}

const alglib::real_1d_array& alglib::real_1d_array::operator=(const alglib::real_1d_array &rhs)
{
    assign(rhs);
    return *this;
}

alglib::real_1d_array::~real_1d_array() 
{
}

const double& alglib::real_1d_array::operator()(ae_int_t i) const
{
    return p_vec->ptr.p_double[i];
}

double& alglib::real_1d_array::operator()(ae_int_t i)
{
    return p_vec->ptr.p_double[i];
}

const double& alglib::real_1d_array::operator[](ae_int_t i) const
{
    return p_vec->ptr.p_double[i];
}

double& alglib::real_1d_array::operator[](ae_int_t i)
{
    return p_vec->ptr.p_double[i];
}

void alglib::real_1d_array::setcontent(ae_int_t iLen, const double *pContent )
{
    ae_int_t i;
    setlength(iLen);
    for(i=0; i<iLen; i++)
        p_vec->ptr.p_double[i] = pContent[i];
}

double* alglib::real_1d_array::getcontent()
{
    return p_vec->ptr.p_double;
}

const double* alglib::real_1d_array::getcontent() const
{
    return p_vec->ptr.p_double;
}

std::string alglib::real_1d_array::tostring(int dps) const 
{
    if( length()==0 )
        return "[]";
    return arraytostring(&operator()(0), length(), dps);
}

alglib::complex_1d_array::complex_1d_array()  
{
    allocate_own(0, alglib_impl::DT_COMPLEX);
}

alglib::complex_1d_array::complex_1d_array(alglib_impl::ae_vector *p)  
{
    p_vec = NULL;
    attach_to(p);
}

alglib::complex_1d_array::complex_1d_array(const char *s)  
{
    create(s, alglib_impl::DT_COMPLEX);
}

alglib::complex_1d_array::complex_1d_array(const alglib::complex_1d_array &rhs)
{
    create(rhs);
}

const alglib::complex_1d_array& alglib::complex_1d_array::operator=(const alglib::complex_1d_array &rhs)
{
    assign(rhs);
    return *this;
}

alglib::complex_1d_array::~complex_1d_array() 
{
}

const alglib::complex& alglib::complex_1d_array::operator()(ae_int_t i) const
{
    return *((const alglib::complex*)(p_vec->ptr.p_complex+i));
}

alglib::complex& alglib::complex_1d_array::operator()(ae_int_t i)
{
    return *((alglib::complex*)(p_vec->ptr.p_complex+i));
}

const alglib::complex& alglib::complex_1d_array::operator[](ae_int_t i) const
{
    return *((const alglib::complex*)(p_vec->ptr.p_complex+i));
}

alglib::complex& alglib::complex_1d_array::operator[](ae_int_t i)
{
    return *((alglib::complex*)(p_vec->ptr.p_complex+i));
}

void alglib::complex_1d_array::setcontent(ae_int_t iLen, const alglib::complex *pContent )
{
    ae_int_t i;
    setlength(iLen);
    for(i=0; i<iLen; i++)
    {
        p_vec->ptr.p_complex[i].x = pContent[i].x;
        p_vec->ptr.p_complex[i].y = pContent[i].y;
    }
}

 alglib::complex* alglib::complex_1d_array::getcontent()
{
    return (alglib::complex*)p_vec->ptr.p_complex;
}

const alglib::complex* alglib::complex_1d_array::getcontent() const
{
    return (const alglib::complex*)p_vec->ptr.p_complex;
}

std::string alglib::complex_1d_array::tostring(int dps) const 
{
    if( length()==0 )
        return "[]";
    return arraytostring(&operator()(0), length(), dps);
}

alglib::ae_matrix_wrapper::ae_matrix_wrapper()
{
    p_mat = NULL;
}

alglib::ae_matrix_wrapper::~ae_matrix_wrapper()
{
    if( p_mat==&mat )
        ae_matrix_clear(p_mat);
}

const alglib::ae_matrix_wrapper& alglib::ae_matrix_wrapper::operator=(const alglib::ae_matrix_wrapper &rhs)
{
    assign(rhs);
    return *this;
}

void alglib::ae_matrix_wrapper::create(const ae_matrix_wrapper &rhs)
{
    if( rhs.p_mat!=NULL )
    {
        p_mat = &mat;
        if( !ae_matrix_init_copy(p_mat, rhs.p_mat, NULL, ae_false) )
            throw alglib::ap_error("ALGLIB: malloc error!");
    }
    else
        p_mat = NULL;
}

void alglib::ae_matrix_wrapper::create(const char *s, alglib_impl::ae_datatype datatype)
{
    std::vector< std::vector<const char*> > smat;
    size_t i, j;
    char *p = filter_spaces(s);
    try
    {
        str_matrix_create(p, &smat);
        if( smat.size()!=0 )
        {
            allocate_own((ae_int_t)(smat.size()), (ae_int_t)(smat[0].size()), datatype);
            for(i=0; i<smat.size(); i++)
                for(j=0; j<smat[0].size(); j++)
                {
                    if( datatype==alglib_impl::DT_BOOL )
                        p_mat->ptr.pp_bool[i][j]    = parse_bool_delim(smat[i][j],",]");
                    if( datatype==alglib_impl::DT_INT )
                        p_mat->ptr.pp_int[i][j]     = parse_int_delim(smat[i][j],",]");
                    if( datatype==alglib_impl::DT_REAL )
                        p_mat->ptr.pp_double[i][j]  = parse_real_delim(smat[i][j],",]");
                    if( datatype==alglib_impl::DT_COMPLEX )
                    {
                        alglib::complex t = parse_complex_delim(smat[i][j],",]");
                        p_mat->ptr.pp_complex[i][j].x = t.x;
                        p_mat->ptr.pp_complex[i][j].y = t.y;
                    }
                }
        }
        else
            allocate_own(0, 0, datatype);
        alglib_impl::ae_free(p);
    }
    catch(...)
    {
        alglib_impl::ae_free(p);
        throw;
    }
}
    
void alglib::ae_matrix_wrapper::assign(const alglib::ae_matrix_wrapper &rhs)
{
    if( this==&rhs )
        return;
    if( p_mat==&mat || p_mat==NULL )
    {
        //
        // Assignment to non-proxy object
        //
        ae_matrix_clear(p_mat);
        if( rhs.p_mat!=NULL )
        {
            p_mat = &mat;
            if( !ae_matrix_init_copy(p_mat, rhs.p_mat, NULL, ae_false) )
                throw alglib::ap_error("ALGLIB: malloc error!");
        }
        else
            p_mat = NULL;
    }
    else
    {
        //
        // Assignment to proxy object
        //
        ae_int_t i;
        if( rhs.p_mat==NULL )
            throw alglib::ap_error("ALGLIB: incorrect assignment to array (sizes dont match)");
        if( rhs.p_mat->datatype!=p_mat->datatype )
            throw alglib::ap_error("ALGLIB: incorrect assignment to array (types dont match)");
        if( rhs.p_mat->rows!=p_mat->rows )
            throw alglib::ap_error("ALGLIB: incorrect assignment to array (sizes dont match)");
        if( rhs.p_mat->cols!=p_mat->cols )
            throw alglib::ap_error("ALGLIB: incorrect assignment to array (sizes dont match)");
        for(i=0; i<p_mat->rows; i++)
            memcpy(p_mat->ptr.pp_void[i], rhs.p_mat->ptr.pp_void[i], p_mat->cols*alglib_impl::ae_sizeof(p_mat->datatype));
    }
}

void alglib::ae_matrix_wrapper::setlength(ae_int_t rows, ae_int_t cols)
{
    if( p_mat==NULL )
        throw alglib::ap_error("ALGLIB: setlength() error, p_mat==NULL (array was not correctly initialized)");
    if( p_mat!=&mat )
        throw alglib::ap_error("ALGLIB: setlength() error, p_mat!=&mat (attempt to resize frozen array)");
    if( !ae_matrix_set_length(p_mat, rows, cols, NULL) )
        throw alglib::ap_error("ALGLIB: malloc error");
}

alglib::ae_int_t alglib::ae_matrix_wrapper::rows() const
{
    if( p_mat==NULL )
        return 0;
    return p_mat->rows;
}

alglib::ae_int_t alglib::ae_matrix_wrapper::cols() const
{
    if( p_mat==NULL )
        return 0;
    return p_mat->cols;
}

bool alglib::ae_matrix_wrapper::isempty() const
{
    return rows()==0 || cols()==0;
}

alglib::ae_int_t alglib::ae_matrix_wrapper::getstride() const
{
    if( p_mat==NULL )
        return 0;
    return p_mat->stride;
}

void alglib::ae_matrix_wrapper::attach_to(alglib_impl::ae_matrix *ptr)
{
    if( ptr==&mat )
        throw alglib::ap_error("ALGLIB: attempt to attach matrix to itself");
    if( p_mat==&mat )
        ae_matrix_clear(p_mat);
    p_mat = ptr;
}

void alglib::ae_matrix_wrapper::allocate_own(ae_int_t rows, ae_int_t cols, alglib_impl::ae_datatype datatype)
{
    if( p_mat==&mat )
        ae_matrix_clear(p_mat);
    p_mat = &mat;
    if( !ae_matrix_init(p_mat, rows, cols, datatype, NULL, false) )
        throw alglib::ap_error("ALGLIB: malloc error");
}

const alglib_impl::ae_matrix* alglib::ae_matrix_wrapper::c_ptr() const
{
    return p_mat;
}

alglib_impl::ae_matrix* alglib::ae_matrix_wrapper::c_ptr()
{
    return p_mat;
}

alglib::boolean_2d_array::boolean_2d_array()  
{
    allocate_own(0, 0, alglib_impl::DT_BOOL);
}

alglib::boolean_2d_array::boolean_2d_array(const alglib::boolean_2d_array &rhs)
{
    create(rhs);
}

alglib::boolean_2d_array::boolean_2d_array(alglib_impl::ae_matrix *p)  
{
    p_mat = NULL;
    attach_to(p);
}

alglib::boolean_2d_array::boolean_2d_array(const char *s)  
{
    create(s, alglib_impl::DT_BOOL);
}

alglib::boolean_2d_array::~boolean_2d_array() 
{
}

const ae_bool& alglib::boolean_2d_array::operator()(ae_int_t i, ae_int_t j) const
{
    return p_mat->ptr.pp_bool[i][j];
}

ae_bool& alglib::boolean_2d_array::operator()(ae_int_t i, ae_int_t j)
{
    return p_mat->ptr.pp_bool[i][j];
}

const ae_bool* alglib::boolean_2d_array::operator[](ae_int_t i) const
{
    return p_mat->ptr.pp_bool[i];
}

ae_bool* alglib::boolean_2d_array::operator[](ae_int_t i)
{
    return p_mat->ptr.pp_bool[i];
}

void alglib::boolean_2d_array::setcontent(ae_int_t irows, ae_int_t icols, const bool *pContent )
{
    ae_int_t i, j;
    setlength(irows, icols);
    for(i=0; i<irows; i++)
        for(j=0; j<icols; j++)
            p_mat->ptr.pp_bool[i][j] = pContent[i*icols+j];
}

std::string alglib::boolean_2d_array::tostring() const 
{
    std::string result;
    ae_int_t i;
    if( isempty() )
        return "[[]]";
    result = "[";
    for(i=0; i<rows(); i++)
    {
        if( i!=0 )
            result += ",";
        result += arraytostring(&operator()(i,0), cols());
    }
    result += "]";
    return result;
}

alglib::integer_2d_array::integer_2d_array()  
{
    allocate_own(0, 0, alglib_impl::DT_INT);
}

alglib::integer_2d_array::integer_2d_array(const alglib::integer_2d_array &rhs)
{
    create(rhs);
}

alglib::integer_2d_array::integer_2d_array(alglib_impl::ae_matrix *p)  
{
    p_mat = NULL;
    attach_to(p);
}

alglib::integer_2d_array::integer_2d_array(const char *s)  
{
    create(s, alglib_impl::DT_INT);
}

alglib::integer_2d_array::~integer_2d_array() 
{
}

const alglib::ae_int_t& alglib::integer_2d_array::operator()(ae_int_t i, ae_int_t j) const
{
    return p_mat->ptr.pp_int[i][j];
}

alglib::ae_int_t& alglib::integer_2d_array::operator()(ae_int_t i, ae_int_t j)
{
    return p_mat->ptr.pp_int[i][j];
}

const alglib::ae_int_t* alglib::integer_2d_array::operator[](ae_int_t i) const
{
    return p_mat->ptr.pp_int[i];
}

alglib::ae_int_t* alglib::integer_2d_array::operator[](ae_int_t i)
{
    return p_mat->ptr.pp_int[i];
}

void alglib::integer_2d_array::setcontent(ae_int_t irows, ae_int_t icols, const ae_int_t *pContent )
{
    ae_int_t i, j;
    setlength(irows, icols);
    for(i=0; i<irows; i++)
        for(j=0; j<icols; j++)
            p_mat->ptr.pp_int[i][j] = pContent[i*icols+j];
}

std::string alglib::integer_2d_array::tostring() const 
{
    std::string result;
    ae_int_t i;
    if( isempty() )
        return "[[]]";
    result = "[";
    for(i=0; i<rows(); i++)
    {
        if( i!=0 )
            result += ",";
        result += arraytostring(&operator()(i,0), cols());
    }
    result += "]";
    return result;
}

alglib::real_2d_array::real_2d_array()  
{
    allocate_own(0, 0, alglib_impl::DT_REAL);
}

alglib::real_2d_array::real_2d_array(const alglib::real_2d_array &rhs)
{
    create(rhs);
}

alglib::real_2d_array::real_2d_array(alglib_impl::ae_matrix *p)
{
    p_mat = NULL;
    attach_to(p);
}

alglib::real_2d_array::real_2d_array(const char *s)  
{
    create(s, alglib_impl::DT_REAL);
}

alglib::real_2d_array::~real_2d_array() 
{
}

const double& alglib::real_2d_array::operator()(ae_int_t i, ae_int_t j) const
{
    return p_mat->ptr.pp_double[i][j];
}

double& alglib::real_2d_array::operator()(ae_int_t i, ae_int_t j)
{
    return p_mat->ptr.pp_double[i][j];
}

const double* alglib::real_2d_array::operator[](ae_int_t i) const
{
    return p_mat->ptr.pp_double[i];
}

double* alglib::real_2d_array::operator[](ae_int_t i)
{
    return p_mat->ptr.pp_double[i];
}

void alglib::real_2d_array::setcontent(ae_int_t irows, ae_int_t icols, const double *pContent )
{
    ae_int_t i, j;
    setlength(irows, icols);
    for(i=0; i<irows; i++)
        for(j=0; j<icols; j++)
            p_mat->ptr.pp_double[i][j] = pContent[i*icols+j];
}

std::string alglib::real_2d_array::tostring(int dps) const 
{
    std::string result;
    ae_int_t i;
    if( isempty() )
        return "[[]]";
    result = "[";
    for(i=0; i<rows(); i++)
    {
        if( i!=0 )
            result += ",";
        result += arraytostring(&operator()(i,0), cols(), dps);
    }
    result += "]";
    return result;
}

alglib::complex_2d_array::complex_2d_array()  
{
    allocate_own(0, 0, alglib_impl::DT_COMPLEX);
}

alglib::complex_2d_array::complex_2d_array(const alglib::complex_2d_array &rhs)
{
    create(rhs);
}

alglib::complex_2d_array::complex_2d_array(alglib_impl::ae_matrix *p)  
{
    p_mat = NULL;
    attach_to(p);
}

alglib::complex_2d_array::complex_2d_array(const char *s)  
{
    create(s, alglib_impl::DT_COMPLEX);
}

alglib::complex_2d_array::~complex_2d_array() 
{
}

const alglib::complex& alglib::complex_2d_array::operator()(ae_int_t i, ae_int_t j) const
{
    return *((const alglib::complex*)(p_mat->ptr.pp_complex[i]+j));
}

alglib::complex& alglib::complex_2d_array::operator()(ae_int_t i, ae_int_t j)
{
    return *((alglib::complex*)(p_mat->ptr.pp_complex[i]+j));
}

const alglib::complex* alglib::complex_2d_array::operator[](ae_int_t i) const
{
    return (const alglib::complex*)(p_mat->ptr.pp_complex[i]);
}

alglib::complex* alglib::complex_2d_array::operator[](ae_int_t i)
{
    return (alglib::complex*)(p_mat->ptr.pp_complex[i]);
}

void alglib::complex_2d_array::setcontent(ae_int_t irows, ae_int_t icols, const alglib::complex *pContent )
{
    ae_int_t i, j;
    setlength(irows, icols);
    for(i=0; i<irows; i++)
        for(j=0; j<icols; j++)
        {
            p_mat->ptr.pp_complex[i][j].x = pContent[i*icols+j].x;
            p_mat->ptr.pp_complex[i][j].y = pContent[i*icols+j].y;
        }
}

std::string alglib::complex_2d_array::tostring(int dps) const 
{
    std::string result;
    ae_int_t i;
    if( isempty() )
        return "[[]]";
    result = "[";
    for(i=0; i<rows(); i++)
    {
        if( i!=0 )
            result += ",";
        result += arraytostring(&operator()(i,0), cols(), dps);
    }
    result += "]";
    return result;
}


/********************************************************************
Internal functions
********************************************************************/
double alglib::get_aenv_nan()
{
    double r;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    r = _alglib_env_state.v_nan;
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return r;
}

double alglib::get_aenv_posinf()
{
    double r;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    r = _alglib_env_state.v_posinf;
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return r;
}

double alglib::get_aenv_neginf()
{
    double r;
    alglib_impl::ae_state _alglib_env_state;
    alglib_impl::ae_state_init(&_alglib_env_state);
    r = _alglib_env_state.v_neginf;
    alglib_impl::ae_state_clear(&_alglib_env_state);
    return r;
}

alglib::ae_int_t alglib::my_stricmp(const char *s1, const char *s2)
{
    int c1, c2;
    
    //
    // handle special cases
    //
    if(s1==NULL && s2!=NULL)
        return -1;
    if(s1!=NULL && s2==NULL)
        return +1;
    if(s1==NULL && s2==NULL)
        return 0;

    //
    // compare
    //
    for (;;)
    {
        c1 = *s1;
        c2 = *s2;
        s1++;
        s2++;
        if( c1==0 )
            return c2==0 ? 0 : -1;
        if( c2==0 )
            return c1==0 ? 0 : +1;
        c1 = tolower(c1);
        c2 = tolower(c2);
        if( c1<c2 )
            return -1;
        if( c1>c2 )
            return +1;
    }
}

char* alglib::filter_spaces(const char *s)
{
    size_t i, n;
    char *r;
    char *r0;
    n = strlen(s);
    r = (char*)alglib_impl::ae_malloc(n+1, NULL);
    if( r==NULL )
        throw ap_error("malloc error");
    for(i=0,r0=r; i<=n; i++,s++)
        if( !isspace(*s) )
        {
            *r0 = *s;
            r0++;
        }
    return r;
}

void alglib::str_vector_create(const char *src, bool match_head_only, std::vector<const char*> *p_vec)
{
    //
    // parse beginning of the string.
    // try to handle "[]" string
    //
    p_vec->clear();
    if( *src!='[' )
        throw alglib::ap_error("Incorrect initializer for vector");
    src++;
    if( *src==']' )
        return;
    p_vec->push_back(src);
    for(;;)
    {
        if( *src==0 )
            throw alglib::ap_error("Incorrect initializer for vector");
        if( *src==']' )
        {
            if( src[1]==0 || !match_head_only)
                return;
            throw alglib::ap_error("Incorrect initializer for vector");
        }
        if( *src==',' )
        {
            p_vec->push_back(src+1);
            src++;
            continue;
        }
        src++;
    }
}

void alglib::str_matrix_create(const char *src, std::vector< std::vector<const char*> > *p_mat)
{
    p_mat->clear();
    
    //
    // Try to handle "[[]]" string
    //
    if( strcmp(src, "[[]]")==0 )
        return;

    //
    // Parse non-empty string
    //
    if( *src!='[' )
        throw alglib::ap_error("Incorrect initializer for matrix");
    src++;
    for(;;)
    {
        p_mat->push_back(std::vector<const char*>());
        str_vector_create(src, false, &p_mat->back());
        if( p_mat->back().size()==0 || p_mat->back().size()!=(*p_mat)[0].size() )
            throw alglib::ap_error("Incorrect initializer for matrix");
        src = strchr(src, ']');
        if( src==NULL )
            throw alglib::ap_error("Incorrect initializer for matrix");
        src++;
        if( *src==',' )
        {
            src++;
            continue;
        }
        if( *src==']' )
            break;
        throw alglib::ap_error("Incorrect initializer for matrix");
    }
    src++;
    if( *src!=0 )
        throw alglib::ap_error("Incorrect initializer for matrix");
}

ae_bool alglib::parse_bool_delim(const char *s, const char *delim)
{
    const char *p;
    char buf[8];
    
    // try to parse false
    p = "false";
    memset(buf, 0, sizeof(buf));
    strncpy(buf, s, strlen(p));
    if( my_stricmp(buf, p)==0 )
    {
        if( s[strlen(p)]==0 || strchr(delim,s[strlen(p)])==NULL )
            throw alglib::ap_error("Cannot parse value");
        return ae_false;
    }

    // try to parse true
    p = "true";
    memset(buf, 0, sizeof(buf));
    strncpy(buf, s, strlen(p));
    if( my_stricmp(buf, p)==0 )
    {
        if( s[strlen(p)]==0 || strchr(delim,s[strlen(p)])==NULL )
            throw alglib::ap_error("Cannot parse value");
        return ae_true;
    }

    // error
    throw alglib::ap_error("Cannot parse value");
}

alglib::ae_int_t alglib::parse_int_delim(const char *s, const char *delim)
{
    const char *p;
    long long_val;
    volatile ae_int_t ae_val;
    
    p = s;

    //
    // check string structure:
    // * leading sign
    // * at least one digit
    // * delimiter
    //
    if( *s=='-' || *s=='+' )
        s++;
    if( *s==0 || strchr("1234567890",*s)==NULL)
        throw alglib::ap_error("Cannot parse value");
    while( *s!=0 && strchr("1234567890",*s)!=NULL )
        s++;
    if( *s==0 || strchr(delim,*s)==NULL )
        throw alglib::ap_error("Cannot parse value");

    // convert and ensure that value fits into ae_int_t
    s = p;
    long_val = atol(s);
    ae_val = long_val;
    if( ae_val!=long_val )
        throw alglib::ap_error("Cannot parse value");
    return ae_val;
}

bool alglib::_parse_real_delim(const char *s, const char *delim, double *result, const char **new_s)
{
    const char *p;
    char *t;
    bool has_digits;
    char buf[64];
    int  isign;
    lconv *loc;

    p = s;
    
    //
    // check string structure and decide what to do
    //
    isign = 1;
    if( *s=='-' || *s=='+' )
    {
        isign = *s=='-' ? -1 : +1;
        s++;
    }
    memset(buf, 0, sizeof(buf));
    strncpy(buf, s, 3);
    if( my_stricmp(buf,"nan")!=0 && my_stricmp(buf,"inf")!=0 )
    {
        //
        // [sign] [ddd] [.] [ddd] [e|E[sign]ddd]
        //
        has_digits = false;
        if( *s!=0 && strchr("1234567890",*s)!=NULL )
        {
            has_digits = true;
            while( *s!=0 && strchr("1234567890",*s)!=NULL )
                s++;
        }
        if( *s=='.' )
            s++;
        if( *s!=0 && strchr("1234567890",*s)!=NULL )
        {
            has_digits = true;
            while( *s!=0 && strchr("1234567890",*s)!=NULL )
                s++;
        }
        if (!has_digits )
            return false;
        if( *s=='e' || *s=='E' )
        {
            s++;
            if( *s=='-' || *s=='+' )
                s++;
            if( *s==0 || strchr("1234567890",*s)==NULL )
                return false;
            while( *s!=0 && strchr("1234567890",*s)!=NULL )
                s++;
        }   
        if( *s==0 || strchr(delim,*s)==NULL )
            return false;
        *new_s = s;

        //
        // finite value conversion
        //
        if( *new_s-p>=(int)sizeof(buf) )
            return false;
        strncpy(buf, p, (size_t)(*new_s-p));
        buf[*new_s-p] = 0;
        loc = localeconv();
        t = strchr(buf,'.');
        if( t!=NULL )
            *t = *loc->decimal_point;
        *result = atof(buf);
        return true;
    }
    else
    {
        //
        // check delimiter and update *new_s
        //
        s += 3;
        if( *s==0 || strchr(delim,*s)==NULL )
            return false;
        *new_s = s;

        //
        // NAN, INF conversion
        //
        if( my_stricmp(buf,"nan")==0 )
            *result = fp_nan;
        if( my_stricmp(buf,"inf")==0 )
            *result = isign>0 ? fp_posinf : fp_neginf;
        return true;
    }
}

double alglib::parse_real_delim(const char *s, const char *delim)
{
    double result;
    const char *new_s;
    if( !_parse_real_delim(s, delim, &result, &new_s) )
        throw alglib::ap_error("Cannot parse value");
    return result;
}

alglib::complex alglib::parse_complex_delim(const char *s, const char *delim)
{
    double d_result;
    const char *new_s;
    alglib::complex c_result;
    
    // parse as real value
    if( _parse_real_delim(s, delim, &d_result, &new_s) )
        return d_result;

    // parse as "a+bi" or "a-bi"
    if( _parse_real_delim(s, "+-", &c_result.x, &new_s) )
    {
        s = new_s;
        if( !_parse_real_delim(s, "i", &c_result.y, &new_s) )
            throw alglib::ap_error("Cannot parse value");
        s = new_s+1;
        if( *s==0 || strchr(delim,*s)==NULL )
            throw alglib::ap_error("Cannot parse value");
        return c_result;
    }
    
    // parse as complex value "bi+a" or "bi-a"
    if( _parse_real_delim(s, "i", &c_result.y, &new_s) )
    {
        s = new_s+1;
        if( *s==0 )
            throw alglib::ap_error("Cannot parse value");
        if( strchr(delim,*s)!=NULL )
        {
            c_result.x = 0;
            return c_result;
        }
        if( strchr("+-",*s)!=NULL )
        {
            if( !_parse_real_delim(s, delim, &c_result.x, &new_s) )
                throw alglib::ap_error("Cannot parse value");
            return c_result;
        }
        throw alglib::ap_error("Cannot parse value");
    }

    // error
    throw alglib::ap_error("Cannot parse value");
}

std::string alglib::arraytostring(const bool *ptr, ae_int_t n)
{
    std::string result;
    ae_int_t i;
    result = "[";
    for(i=0; i<n; i++)
    {
        if( i!=0 )
            result += ",";
        result += ptr[i] ? "true" : "false";
    }
    result += "]";
    return result;
}

std::string alglib::arraytostring(const ae_int_t *ptr, ae_int_t n)
{
    std::string result;
    ae_int_t i;
    char buf[64];
    result = "[";
    for(i=0; i<n; i++)
    {
        if( sprintf(buf, i==0 ? "%ld" : ",%ld", long(ptr[i]))>=(int)sizeof(buf) )
            throw ap_error("arraytostring(): buffer overflow");
        result += buf;
    }
    result += "]";
    return result;
}

std::string alglib::arraytostring(const double *ptr, ae_int_t n, int _dps)
{
    std::string result;
    ae_int_t i;
    char buf[64];
    char mask1[64];
    char mask2[64];
    int dps = _dps>=0 ? _dps : -_dps;
    result = "[";
    if( sprintf(mask1, "%%.%d%s", dps, _dps>=0 ? "f" : "e")>=(int)sizeof(mask1) )
        throw ap_error("arraytostring(): buffer overflow");
    if( sprintf(mask2, ",%s", mask1)>=(int)sizeof(mask2) )
        throw ap_error("arraytostring(): buffer overflow");
    for(i=0; i<n; i++)
    {
        buf[0] = 0;
        if( fp_isfinite(ptr[i]) )
        {
            if( sprintf(buf, i==0 ? mask1 : mask2, double(ptr[i]))>=(int)sizeof(buf) )
                throw ap_error("arraytostring(): buffer overflow");
        }
        else if( fp_isnan(ptr[i]) )
            strcpy(buf, i==0 ?  "NAN" :  ",NAN");
        else if( fp_isposinf(ptr[i]) )
            strcpy(buf, i==0 ? "+INF" : ",+INF");
        else if( fp_isneginf(ptr[i]) )
            strcpy(buf, i==0 ? "-INF" : ",-INF");
        result += buf;
    }
    result += "]";
    return result;
}

std::string alglib::arraytostring(const alglib::complex *ptr, ae_int_t n, int dps)
{
    std::string result;
    ae_int_t i;
    result = "[";
    for(i=0; i<n; i++)
    {
        if( i!=0 )
            result += ",";
        result += ptr[i].tostring(dps);
    }
    result += "]";
    return result;
}


/********************************************************************
standard functions
********************************************************************/
int alglib::sign(double x)
{
    if( x>0 ) return  1;
    if( x<0 ) return -1;
    return 0;
}

double alglib::randomreal()
{
    int i1 = rand();
    int i2 = rand();
    double mx = (double)(RAND_MAX)+1.0;
    volatile double tmp0 = i2/mx;
    volatile double tmp1 = i1+tmp0;
    return tmp1/mx;
}

alglib::ae_int_t alglib::randominteger(alglib::ae_int_t maxv)
{
    return ((alglib::ae_int_t)rand())%maxv;
}

int alglib::round(double x)
{ return int(floor(x+0.5)); }

int alglib::trunc(double x)
{ return int(x>0 ? floor(x) : ceil(x)); }

int alglib::ifloor(double x)
{ return int(floor(x)); }

int alglib::iceil(double x)
{ return int(ceil(x)); }

double alglib::pi()
{ return 3.14159265358979323846; }

double alglib::sqr(double x)
{ return x*x; }

int alglib::maxint(int m1, int m2)
{
    return m1>m2 ? m1 : m2;
}

int alglib::minint(int m1, int m2)
{
    return m1>m2 ? m2 : m1;
}

double alglib::maxreal(double m1, double m2)
{
    return m1>m2 ? m1 : m2;
}

double alglib::minreal(double m1, double m2)
{
    return m1>m2 ? m2 : m1;
}

bool alglib::fp_eq(double v1, double v2)
{
    // IEEE-strict floating point comparison
    volatile double x = v1;
    volatile double y = v2;
    return x==y;
}

bool alglib::fp_neq(double v1, double v2)
{
    // IEEE-strict floating point comparison
    return !fp_eq(v1,v2);
}

bool alglib::fp_less(double v1, double v2)
{
    // IEEE-strict floating point comparison
    volatile double x = v1;
    volatile double y = v2;
    return x<y;
}

bool alglib::fp_less_eq(double v1, double v2)
{
    // IEEE-strict floating point comparison
    volatile double x = v1;
    volatile double y = v2;
    return x<=y;
}

bool alglib::fp_greater(double v1, double v2)
{
    // IEEE-strict floating point comparison
    volatile double x = v1;
    volatile double y = v2;
    return x>y;
}

bool alglib::fp_greater_eq(double v1, double v2)
{
    // IEEE-strict floating point comparison
    volatile double x = v1;
    volatile double y = v2;
    return x>=y;
}

bool alglib::fp_isnan(double x)
{
    return alglib_impl::ae_isnan_stateless(x,endianness);
}

bool alglib::fp_isposinf(double x)
{
    return alglib_impl::ae_isposinf_stateless(x,endianness);
}

bool alglib::fp_isneginf(double x)
{
    return alglib_impl::ae_isneginf_stateless(x,endianness);
}

bool alglib::fp_isinf(double x)
{
    return alglib_impl::ae_isinf_stateless(x,endianness);
}

bool alglib::fp_isfinite(double x)
{
    return alglib_impl::ae_isfinite_stateless(x,endianness);
}

/********************************************************************
Dataset functions
********************************************************************/
/*bool alglib::readstrings(std::string file, std::list<std::string> *pOutput)
{
    return readstrings(file, pOutput, "");
}

bool alglib::readstrings(std::string file, std::list<std::string> *pOutput, std::string comment)
{
    std::string cmd, s;
    FILE *f;
    char buf[32768];
    char *str;

    f = fopen(file.c_str(), "rb");
    if( !f )
        return false;
    s = "";
    pOutput->clear();
    while(str=fgets(buf, sizeof(buf), f))
    {
        // TODO: read file by small chunks, combine in one large string
        if( strlen(str)==0 )
            continue;
            
        //
        // trim trailing newline chars
        //
        char *eos = str+strlen(str)-1;
        if( *eos=='\n' )
        {
            *eos = 0;
            eos--;
        }
        if( *eos=='\r' )
        {
            *eos = 0;
            eos--;
        }
        s = str;

        //
        // skip comments
        //
        if( comment.length()>0 )
            if( strncmp(s.c_str(), comment.c_str(), comment.length())==0 )
            {
                s = "";
                continue;
            }

        //
        // read data
        //
        if( s.length()<1 )
        {
            fclose(f);
            throw alglib::ap_error("internal error in read_strings");
        }
        pOutput->push_back(s);
    }
    fclose(f);
    return true;
}

void alglib::explodestring(std::string s, char sep, std::vector<std::string> *pOutput)
{
    std::string tmp;
    int i;
    tmp = "";
    pOutput->clear();
    for(i=0; i<s.length(); i++)
    {
        if( s[i]!=sep )
        {
            tmp += s[i];
            continue;
        }
        //if( tmp.length()!=0 )
        pOutput->push_back(tmp);
        tmp = "";
    }
    if( tmp.length()!=0 )
        pOutput->push_back(tmp);
}

std::string alglib::strtolower(const std::string &s)
{
    std::string r = s;
    for(int i=0; i<r.length(); i++)
        r[i] = tolower(r[i]);
    return r;
}

std::string alglib::xtrim(std::string s)
{
    char *pstr = (char*)malloc(s.length()+1);
    char *p2 = pstr;
    if( pstr==NULL )
        throw "xalloc in xtrim()";
    try
    {
        bool bws;
        int i;

        //
        // special cases:
        // * zero length string
        // * string includes only spaces
        //
        if( s.length()==0 )
        {
            free(pstr);
            return "";
        }
        bws = true;
        for(i=0; i<s.length(); i++)
            if( s[i]!=' ' )
                bws = false;
        if( bws )
        {
            free(pstr);
            return "";
        }

        //
        // merge internal spaces
        //
        bws = false;
        for(i=0; i<s.length(); i++)
        {
            if( s[i]==' ' && bws )
                continue;
            if( s[i]==' ' )
            {
                *p2 = ' ';
                p2++;
                bws = true;
                continue;
            }
            *p2 = s[i];
            bws = false;
            p2++;
        }
        *p2 = 0;

        //
        // trim leading/trailing spaces.
        // we expect at least one non-space character in the string
        //
        p2--;
        while(*p2==' ')
        {
            *p2 = 0;
            p2--;
        }
        p2 = pstr;
        while((*p2)==' ')
            p2++;

        //
        // result
        //
        std::string r = p2;
        free(pstr);
        return r;
    }
    catch(...)
    {
        free(pstr);
        throw "unknown exception in xtrim()";
    }
}

bool alglib::opendataset(std::string file, dataset *pdataset)
{
    std::list<std::string> Lines;
    std::vector<std::string> Values, RowsArr, ColsArr, VarsArr, HeadArr;
    std::list<std::string>::iterator i;
    std::string s;
    int TrnFirst, TrnLast, ValFirst, ValLast, TstFirst, TstLast, LinesRead, j;

    //
    // Read data
    //
    if( pdataset==NULL )
        return false;
    if( !readstrings(file, &Lines, "//") )
        return false;
    i = Lines.begin();
    *pdataset = dataset();

    //
    // Read header
    //
    if( i==Lines.end() )
        return false;
    s = alglib::xtrim(*i);
    alglib::explodestring(s, '#', &HeadArr);
    if( HeadArr.size()!=2 )
        return false;

    //
    // Rows info
    //
    alglib::explodestring(alglib::xtrim(HeadArr[0]), ' ', &RowsArr);
    if( RowsArr.size()==0 || RowsArr.size()>3 )
        return false;
    if( RowsArr.size()==1 )
    {
        pdataset->totalsize = atol(RowsArr[0].c_str());
        pdataset->trnsize = pdataset->totalsize;
    }
    if( RowsArr.size()==2 )
    {
        pdataset->trnsize = atol(RowsArr[0].c_str());
        pdataset->tstsize = atol(RowsArr[1].c_str());
        pdataset->totalsize = pdataset->trnsize + pdataset->tstsize;
    }
    if( RowsArr.size()==3 )
    {
        pdataset->trnsize = atol(RowsArr[0].c_str());
        pdataset->valsize = atol(RowsArr[1].c_str());
        pdataset->tstsize = atol(RowsArr[2].c_str());
        pdataset->totalsize = pdataset->trnsize + pdataset->valsize + pdataset->tstsize;
    }
    if( pdataset->totalsize<=0 || pdataset->trnsize<0 || pdataset->valsize<0 || pdataset->tstsize<0 )
        return false;
    TrnFirst = 0;
    TrnLast = TrnFirst + pdataset->trnsize;
    ValFirst = TrnLast;
    ValLast = ValFirst + pdataset->valsize;
    TstFirst = ValLast;
    TstLast = TstFirst + pdataset->tstsize;
                
    //
    // columns
    //
    alglib::explodestring(alglib::xtrim(HeadArr[1]), ' ', &ColsArr);
    if( ColsArr.size()!=1 && ColsArr.size()!=4 )
        return false;
    if( ColsArr.size()==1 )
    {
        pdataset->nin = atoi(ColsArr[0].c_str());
        if( pdataset->nin<=0 )
            return false;
    }
    if( ColsArr.size()==4 )
    {
        if( alglib::strtolower(ColsArr[0])!="reg" && alglib::strtolower(ColsArr[0])!="cls" )
            return false;
        if( ColsArr[2]!="=>" )
            return false;
        pdataset->nin = atol(ColsArr[1].c_str());
        if( pdataset->nin<1 )
            return false;
        if( alglib::strtolower(ColsArr[0])=="reg" )
        {
            pdataset->nclasses = 0;
            pdataset->nout = atol(ColsArr[3].c_str());
            if( pdataset->nout<1 )
                return false;
        }
        else
        {
            pdataset->nclasses = atol(ColsArr[3].c_str());
            pdataset->nout = 1;
            if( pdataset->nclasses<2 )
                return false;
        }
    }

    //
    // initialize arrays
    //
    pdataset->all.setlength(pdataset->totalsize, pdataset->nin+pdataset->nout);
    if( pdataset->trnsize>0 ) pdataset->trn.setlength(pdataset->trnsize, pdataset->nin+pdataset->nout);
    if( pdataset->valsize>0 ) pdataset->val.setlength(pdataset->valsize, pdataset->nin+pdataset->nout);
    if( pdataset->tstsize>0 ) pdataset->tst.setlength(pdataset->tstsize, pdataset->nin+pdataset->nout);

    //
    // read data
    //
    for(LinesRead=0, i++; i!=Lines.end() && LinesRead<pdataset->totalsize; i++, LinesRead++)
    {
        std::string sss = *i;
        alglib::explodestring(alglib::xtrim(*i), ' ', &VarsArr);
        if( VarsArr.size()!=pdataset->nin+pdataset->nout )
            return false;
        int tmpc = alglib::round(atof(VarsArr[pdataset->nin+pdataset->nout-1].c_str()));
        if( pdataset->nclasses>0 && (tmpc<0 || tmpc>=pdataset->nclasses) )
            return false;
        for(j=0; j<pdataset->nin+pdataset->nout; j++)
        {
            pdataset->all(LinesRead,j) = atof(VarsArr[j].c_str());
            if( LinesRead>=TrnFirst && LinesRead<TrnLast )
                pdataset->trn(LinesRead-TrnFirst,j) = atof(VarsArr[j].c_str());
            if( LinesRead>=ValFirst && LinesRead<ValLast )
                pdataset->val(LinesRead-ValFirst,j) = atof(VarsArr[j].c_str());
            if( LinesRead>=TstFirst && LinesRead<TstLast )
                pdataset->tst(LinesRead-TstFirst,j) = atof(VarsArr[j].c_str());
        }
    }
    if( LinesRead!=pdataset->totalsize )
        return false;
    return true;
}*/

/*
previous variant
bool alglib::opendataset(std::string file, dataset *pdataset)
{
    std::list<std::string> Lines;
    std::vector<std::string> Values;
    std::list<std::string>::iterator i;
    int nCol, nRow, nSplitted;
    int nColumns, nRows;

    //
    // Read data
    //
    if( pdataset==NULL )
        return false;
    if( !readstrings(file, &Lines, "//") )
        return false;
    i = Lines.begin();
    *pdataset = dataset();

    //
    // Read columns info
    //
    if( i==Lines.end() )
        return false;
    if( sscanf(i->c_str(), " columns = %d %d ", &pdataset->nin, &pdataset->nout)!=2 )
        return false;
    if( pdataset->nin<=0 || pdataset->nout==0 || pdataset->nout==-1)
        return false;
    if( pdataset->nout<0 )
    {
        pdataset->nclasses = -pdataset->nout;
        pdataset->nout = 1;
        pdataset->iscls = true;
    }
    else
    {
        pdataset->isreg = true;
    }
    nColumns = pdataset->nin+pdataset->nout;
    i++;

    //
    // Read rows info
    //
    if( i==Lines.end() )
        return false;
    if( sscanf(i->c_str(), " rows = %d %d %d ", &pdataset->trnsize, &pdataset->valsize, &pdataset->tstsize)!=3 )
        return false;
    if( (pdataset->trnsize<0) || (pdataset->valsize<0) || (pdataset->tstsize<0) )
        return false;
    if( (pdataset->trnsize==0) && (pdataset->valsize==0) && (pdataset->tstsize==0) )
        return false;
    nRows = pdataset->trnsize+pdataset->valsize+pdataset->tstsize;
    pdataset->size = nRows;
    if( Lines.size()!=nRows+2 )
        return false;
    i++;

    //
    // Read all cases
    //
    alglib::real_2d_array &arr = pdataset->all;
    arr.setbounds(0, nRows-1, 0, nColumns-1);
    for(nRow=0; nRow<nRows; nRow++)
    {
        alglib::ap_error::make_assertion(i!=Lines.end());
        explodestring(*i, '\t', &Values);
        if( Values.size()!=nColumns )
            return false;
        for(nCol=0; nCol<nColumns; nCol++)
        {
            double v;
            if( sscanf(Values[nCol].c_str(), "%lg", &v)!=1 )
                return false;
            if( (nCol==nColumns-1) && pdataset->iscls && ((round(v)<0) || (round(v)>=pdataset->nclasses)) )
                return false;
            if( (nCol==nColumns-1) && pdataset->iscls )
                arr(nRow, nCol) = round(v);
            else
                arr(nRow, nCol) = v;
        }
        i++;
    }

    //
    // Split to training, validation and test sets
    //
    if( pdataset->trnsize>0 )
        pdataset->trn.setbounds(0, pdataset->trnsize-1, 0, nColumns-1);
    if( pdataset->valsize>0 )
        pdataset->val.setbounds(0, pdataset->valsize-1, 0, nColumns-1);
    if( pdataset->tstsize>0 )
        pdataset->tst.setbounds(0, pdataset->tstsize-1, 0, nColumns-1);
    nSplitted=0;
    for(nRow=0; nRow<=pdataset->trnsize-1; nRow++, nSplitted++)
        for(nCol=0; nCol<=nColumns-1; nCol++)
            pdataset->trn(nRow,nCol) = arr(nSplitted,nCol);
    for(nRow=0; nRow<=pdataset->valsize-1; nRow++, nSplitted++)
        for(nCol=0; nCol<=nColumns-1; nCol++)
            pdataset->val(nRow,nCol) = arr(nSplitted,nCol);
    for(nRow=0; nRow<=pdataset->tstsize-1; nRow++, nSplitted++)
        for(nCol=0; nCol<=nColumns-1; nCol++)
            pdataset->tst(nRow,nCol) = arr(nSplitted,nCol);
    return true;
}*/

alglib::ae_int_t alglib::vlen(ae_int_t n1, ae_int_t n2)
{
    return n2-n1+1;
}



/////////////////////////////////////////////////////////////////////////
//
// THIS SECTIONS CONTAINS OPTIMIZED LINEAR ALGEBRA CODE
// IT IS SHARED BETWEEN C++ AND PURE C LIBRARIES
//
/////////////////////////////////////////////////////////////////////////
namespace alglib_impl
{
#define alglib_simd_alignment 16

#define alglib_r_block        32
#define alglib_half_r_block   16
#define alglib_twice_r_block  64

#define alglib_c_block        24
#define alglib_half_c_block   12
#define alglib_twice_c_block  48


/********************************************************************
This subroutine calculates fast 32x32 real matrix-vector product:

    y := beta*y + alpha*A*x

using either generic C code or native optimizations (if available)

IMPORTANT:
* A must be stored in row-major order,
  stride is alglib_r_block,
  aligned on alglib_simd_alignment boundary
* X must be aligned on alglib_simd_alignment boundary
* Y may be non-aligned
********************************************************************/
void _ialglib_mv_32(const double *a, const double *x, double *y, ae_int_t stride, double alpha, double beta)
{
    ae_int_t i, k;
    const double *pa0, *pa1, *pb;

    pa0 = a;
    pa1 = a+alglib_r_block;
    pb = x;
    for(i=0; i<16; i++)
    {
        double v0 = 0, v1 = 0;
        for(k=0; k<4; k++)
        {
            v0 += pa0[0]*pb[0];
            v1 += pa1[0]*pb[0];
            v0 += pa0[1]*pb[1];
            v1 += pa1[1]*pb[1];
            v0 += pa0[2]*pb[2];
            v1 += pa1[2]*pb[2];
            v0 += pa0[3]*pb[3];
            v1 += pa1[3]*pb[3];
            v0 += pa0[4]*pb[4];
            v1 += pa1[4]*pb[4];
            v0 += pa0[5]*pb[5];
            v1 += pa1[5]*pb[5];
            v0 += pa0[6]*pb[6];
            v1 += pa1[6]*pb[6];
            v0 += pa0[7]*pb[7];
            v1 += pa1[7]*pb[7];
            pa0 += 8;
            pa1 += 8;
            pb  += 8;
        }
        y[0] = beta*y[0]+alpha*v0;
        y[stride] = beta*y[stride]+alpha*v1;

        /*
         * now we've processed rows I and I+1,
         * pa0 and pa1 are pointing to rows I+1 and I+2.
         * move to I+2 and I+3.
         */
        pa0 += alglib_r_block;
        pa1 += alglib_r_block;
        pb = x;
        y+=2*stride;
    }
}


/*************************************************************************
This function calculates MxN real matrix-vector product:

    y := beta*y + alpha*A*x

using generic C code. It calls _ialglib_mv_32 if both M=32 and N=32.

If beta is zero, we do not use previous values of y (they are  overwritten
by alpha*A*x without ever being read).  If alpha is zero, no matrix-vector
product is calculated (only beta is updated); however, this update  is not
efficient  and  this  function  should  NOT  be used for multiplication of 
vector and scalar.

IMPORTANT:
* 0<=M<=alglib_r_block, 0<=N<=alglib_r_block
* A must be stored in row-major order with stride equal to alglib_r_block
*************************************************************************/
void _ialglib_rmv(ae_int_t m, ae_int_t n, const double *a, const double *x, double *y, ae_int_t stride, double alpha, double beta)
{
    /*
     * Handle special cases:
     * - alpha is zero or n is zero
     * - m is zero
     */
    if( m==0 )
        return;
    if( alpha==0.0 || n==0 )
    {
        ae_int_t i;
        if( beta==0.0 )
        {
            for(i=0; i<m; i++)
            {
                *y = 0.0;
                y += stride;
            }
        }
        else
        {
            for(i=0; i<m; i++)
            {
                *y *= beta;
                y += stride;
            }
        }
        return;
    }
    
    /*
     * Handle general case: nonzero alpha, n and m
     *
     */
    if( m==32 && n==32 )
    {
        /*
         * 32x32, may be we have something better than general implementation
         */
        _ialglib_mv_32(a, x, y, stride, alpha, beta);
    }
    else
    {
        ae_int_t i, k, m2, n8, n2, ntrail2;
        const double *pa0, *pa1, *pb;

        /*
         * First M/2 rows of A are processed in pairs.
         * optimized code is used.
         */
        m2 = m/2;
        n8 = n/8;
        ntrail2 = (n-8*n8)/2;
        for(i=0; i<m2; i++)
        {
            double v0 = 0, v1 = 0;

            /*
             * 'a' points to the part of the matrix which
             * is not processed yet
             */
            pb = x;
            pa0 = a;
            pa1 = a+alglib_r_block;
            a += alglib_twice_r_block;

            /*
             * 8 elements per iteration
             */
            for(k=0; k<n8; k++)
            {
                v0 += pa0[0]*pb[0];
                v1 += pa1[0]*pb[0];
                v0 += pa0[1]*pb[1];
                v1 += pa1[1]*pb[1];
                v0 += pa0[2]*pb[2];
                v1 += pa1[2]*pb[2];
                v0 += pa0[3]*pb[3];
                v1 += pa1[3]*pb[3];
                v0 += pa0[4]*pb[4];
                v1 += pa1[4]*pb[4];
                v0 += pa0[5]*pb[5];
                v1 += pa1[5]*pb[5];
                v0 += pa0[6]*pb[6];
                v1 += pa1[6]*pb[6];
                v0 += pa0[7]*pb[7];
                v1 += pa1[7]*pb[7];
                pa0 += 8;
                pa1 += 8;
                pb  += 8;
            }

            /*
             * 2 elements per iteration
             */
            for(k=0; k<ntrail2; k++)
            {
                v0 += pa0[0]*pb[0];
                v1 += pa1[0]*pb[0];
                v0 += pa0[1]*pb[1];
                v1 += pa1[1]*pb[1];
                pa0 += 2;
                pa1 += 2;
                pb  += 2;
            }

            /*
             * last element, if needed
             */
            if( n%2!=0 )
            {
                v0 += pa0[0]*pb[0];
                v1 += pa1[0]*pb[0];
            }

            /*
             * final update
             */
            if( beta!=0 )
            {
                y[0] = beta*y[0]+alpha*v0;
                y[stride] = beta*y[stride]+alpha*v1;
            }
            else
            {
                y[0] = alpha*v0;
                y[stride] = alpha*v1;
            }
            
            /*
             * move to the next pair of elements
             */
            y+=2*stride;
        }


        /*
         * Last (odd) row is processed with less optimized code.
         */
        if( m%2!=0 )
        {
            double v0 = 0;

            /*
             * 'a' points to the part of the matrix which
             * is not processed yet
             */
            pb = x;
            pa0 = a;

            /*
             * 2 elements per iteration
             */
            n2 = n/2;
            for(k=0; k<n2; k++)
            {
                v0 += pa0[0]*pb[0]+pa0[1]*pb[1];
                pa0 += 2;
                pb  += 2;
            }

            /*
             * last element, if needed
             */
            if( n%2!=0 )
                v0 += pa0[0]*pb[0];

            /*
             * final update
             */
            if( beta!=0 )
                y[0] = beta*y[0]+alpha*v0;
            else
                y[0] = alpha*v0;
        }
    }
}


/*************************************************************************
This function calculates MxN real matrix-vector product:

    y := beta*y + alpha*A*x

using generic C code. It calls _ialglib_mv_32 if both M=32 and N=32.

If beta is zero, we do not use previous values of y (they are  overwritten
by alpha*A*x without ever being read).  If alpha is zero, no matrix-vector
product is calculated (only beta is updated); however, this update  is not
efficient  and  this  function  should  NOT  be used for multiplication of 
vector and scalar.

IMPORTANT:
* 0<=M<=alglib_r_block, 0<=N<=alglib_r_block
* A must be stored in row-major order with stride equal to alglib_r_block
* y may be non-aligned
* both A and x must have same offset with respect to 16-byte boundary:
  either both are aligned, or both are aligned with offset 8. Function
  will crash your system if you try to call it with misaligned or 
  incorrectly aligned data.

This function supports SSE2; it can be used when:
1. AE_HAS_SSE2_INTRINSICS was defined (checked at compile-time)
2. ae_cpuid() result contains CPU_SSE2 (checked at run-time)

If (1) is failed, this function will be undefined. If (2) is failed,  call 
to this function will probably crash your system. 

If  you  want  to  know  whether  it  is safe to call it, you should check 
results  of  ae_cpuid(). If CPU_SSE2 bit is set, this function is callable 
and will do its work.
*************************************************************************/
#if defined(AE_HAS_SSE2_INTRINSICS)
void _ialglib_rmv_sse2(ae_int_t m, ae_int_t n, const double *a, const double *x, double *y, ae_int_t stride, double alpha, double beta)
{
    ae_int_t i, k, n2;
    ae_int_t mb3, mtail, nhead, nb8, nb2, ntail;
    const double *pa0, *pa1, *pa2, *pb;
    __m128d v0, v1, v2, va0, va1, va2, vx, vtmp; 
    double buf3[3], buf6[6];
    double d;
    
    /*
     * Handle special cases:
     * - alpha is zero or n is zero
     * - m is zero
     */
    if( m==0 )
        return;
    if( alpha==0.0 || n==0 )
    {
        if( beta==0.0 )
        {
            for(i=0; i<m; i++)
            {
                *y = 0.0;
                y += stride;
            }
        }
        else
        {
            for(i=0; i<m; i++)
            {
                *y *= beta;
                y += stride;
            }
        }
        return;
    }
    
    /*
     * Handle general case: nonzero alpha, n and m
     *
     * We divide problem as follows...
     *
     * Rows M are divided into:
     * - mb3 blocks, each 3xN
     * - mtail blocks, each 1xN
     *
     * Within a row, elements are divided  into:
     * - nhead 1x1 blocks (used to align the rest, either 0 or 1)
     * - nb8 1x8 blocks, aligned to 16-byte boundary
     * - nb2 1x2 blocks, aligned to 16-byte boundary
     * - ntail 1x1 blocks, aligned too (altough we don't rely on it)
     *
     */
    n2 = n/2;    
    mb3 = m/3;
    mtail = m%3;
    nhead = ae_misalignment(a,alglib_simd_alignment)==0 ? 0 : 1;
    nb8 = (n-nhead)/8;
    nb2 = (n-nhead-8*nb8)/2;
    ntail = n-nhead-8*nb8-2*nb2;
    for(i=0; i<mb3; i++)
    {
        double row0, row1, row2;
        row0 = 0;
        row1 = 0;
        row2 = 0;
        pb = x;
        pa0 = a;
        pa1 = a+alglib_r_block;
        pa2 = a+alglib_twice_r_block;
        a += 3*alglib_r_block;
        if( nhead==1 )
        {
            vx  = _mm_load_sd(pb);
            v0 = _mm_load_sd(pa0);
            v1 = _mm_load_sd(pa1);
            v2 = _mm_load_sd(pa2);
            
            v0 = _mm_mul_sd(v0,vx);
            v1 = _mm_mul_sd(v1,vx);
            v2 = _mm_mul_sd(v2,vx);
            
            pa0++;
            pa1++;
            pa2++;
            pb++;
        }
        else
        {
            v0 = _mm_setzero_pd();
            v1 = _mm_setzero_pd();
            v2 = _mm_setzero_pd();
        }
        for(k=0; k<nb8; k++)
        {
            /*
             * this code is a shuffle of simultaneous dot product.
             * see below for commented unshuffled original version.
             */
            vx  = _mm_load_pd(pb);
            va0 = _mm_load_pd(pa0);
            va1 = _mm_load_pd(pa1);
            va0 = _mm_mul_pd(va0,vx);
            va2 = _mm_load_pd(pa2);
            v0 = _mm_add_pd(va0,v0);
            va1 = _mm_mul_pd(va1,vx);
            va0 = _mm_load_pd(pa0+2);
            v1 = _mm_add_pd(va1,v1);
            va2 = _mm_mul_pd(va2,vx);
            va1 = _mm_load_pd(pa1+2);
            v2 = _mm_add_pd(va2,v2);
            vx  = _mm_load_pd(pb+2);
            va0 = _mm_mul_pd(va0,vx);
            va2 = _mm_load_pd(pa2+2);
            v0 = _mm_add_pd(va0,v0);
            va1 = _mm_mul_pd(va1,vx);
            va0 = _mm_load_pd(pa0+4);
            v1 = _mm_add_pd(va1,v1);
            va2 = _mm_mul_pd(va2,vx);
            va1 = _mm_load_pd(pa1+4);
            v2 = _mm_add_pd(va2,v2);
            vx  = _mm_load_pd(pb+4);
            va0 = _mm_mul_pd(va0,vx);
            va2 = _mm_load_pd(pa2+4);
            v0 = _mm_add_pd(va0,v0);
            va1 = _mm_mul_pd(va1,vx);
            va0 = _mm_load_pd(pa0+6);
            v1 = _mm_add_pd(va1,v1);
            va2 = _mm_mul_pd(va2,vx);
            va1 = _mm_load_pd(pa1+6);
            v2 = _mm_add_pd(va2,v2);
            vx  = _mm_load_pd(pb+6);
            va0 = _mm_mul_pd(va0,vx);
            v0 = _mm_add_pd(va0,v0);
            va2 = _mm_load_pd(pa2+6);
            va1 = _mm_mul_pd(va1,vx);
            v1 = _mm_add_pd(va1,v1);
            va2 = _mm_mul_pd(va2,vx);
            v2 = _mm_add_pd(va2,v2);
            
            pa0 += 8;
            pa1 += 8;
            pa2 += 8;
            pb += 8;

            /*
            this is unshuffled version of code above
            
            vx  = _mm_load_pd(pb);
            va0 = _mm_load_pd(pa0);            
            va1 = _mm_load_pd(pa1);
            va2 = _mm_load_pd(pa2);
            
            va0 = _mm_mul_pd(va0,vx);
            va1 = _mm_mul_pd(va1,vx);
            va2 = _mm_mul_pd(va2,vx);
            
            v0 = _mm_add_pd(va0,v0);
            v1 = _mm_add_pd(va1,v1);
            v2 = _mm_add_pd(va2,v2);
            
            vx  = _mm_load_pd(pb+2);
            va0 = _mm_load_pd(pa0+2);            
            va1 = _mm_load_pd(pa1+2);
            va2 = _mm_load_pd(pa2+2);
            
            va0 = _mm_mul_pd(va0,vx);
            va1 = _mm_mul_pd(va1,vx);
            va2 = _mm_mul_pd(va2,vx);
            
            v0 = _mm_add_pd(va0,v0);
            v1 = _mm_add_pd(va1,v1);
            v2 = _mm_add_pd(va2,v2);

            vx  = _mm_load_pd(pb+4);
            va0 = _mm_load_pd(pa0+4);            
            va1 = _mm_load_pd(pa1+4);
            va2 = _mm_load_pd(pa2+4);
            
            va0 = _mm_mul_pd(va0,vx);
            va1 = _mm_mul_pd(va1,vx);
            va2 = _mm_mul_pd(va2,vx);
            
            v0 = _mm_add_pd(va0,v0);
            v1 = _mm_add_pd(va1,v1);
            v2 = _mm_add_pd(va2,v2);

            vx  = _mm_load_pd(pb+6);
            va0 = _mm_load_pd(pa0+6);
            va1 = _mm_load_pd(pa1+6);
            va2 = _mm_load_pd(pa2+6);
            
            va0 = _mm_mul_pd(va0,vx);
            va1 = _mm_mul_pd(va1,vx);
            va2 = _mm_mul_pd(va2,vx);
            
            v0 = _mm_add_pd(va0,v0);
            v1 = _mm_add_pd(va1,v1);
            v2 = _mm_add_pd(va2,v2);
            */
        }
        for(k=0; k<nb2; k++)
        {
            vx  = _mm_load_pd(pb);
            va0 = _mm_load_pd(pa0);
            va1 = _mm_load_pd(pa1);
            va2 = _mm_load_pd(pa2);
            
            va0 = _mm_mul_pd(va0,vx);
            v0 = _mm_add_pd(va0,v0);
            va1 = _mm_mul_pd(va1,vx);
            v1 = _mm_add_pd(va1,v1);
            va2 = _mm_mul_pd(va2,vx);
            v2 = _mm_add_pd(va2,v2);
            
            pa0 += 2;
            pa1 += 2;
            pa2 += 2;
            pb += 2;
        }
        for(k=0; k<ntail; k++)
        {
            vx  = _mm_load1_pd(pb);
            va0 = _mm_load1_pd(pa0);
            va1 = _mm_load1_pd(pa1);
            va2 = _mm_load1_pd(pa2);
            
            va0 = _mm_mul_sd(va0,vx);
            v0 = _mm_add_sd(v0,va0);
            va1 = _mm_mul_sd(va1,vx);
            v1 = _mm_add_sd(v1,va1);
            va2 = _mm_mul_sd(va2,vx);
            v2 = _mm_add_sd(v2,va2);
        }        
        vtmp = _mm_add_pd(_mm_unpacklo_pd(v0,v1),_mm_unpackhi_pd(v0,v1));
        _mm_storel_pd(&row0, vtmp);
        _mm_storeh_pd(&row1, vtmp);
        v2 = _mm_add_sd(_mm_shuffle_pd(v2,v2,1),v2);
        _mm_storel_pd(&row2, v2);
        if( beta!=0 )
        {
            y[0] = beta*y[0]+alpha*row0;
            y[stride] = beta*y[stride]+alpha*row1;
            y[2*stride] = beta*y[2*stride]+alpha*row2;
        }
        else
        {
            y[0] = alpha*row0;
            y[stride] = alpha*row1;
            y[2*stride] = alpha*row2;
        }
        y+=3*stride;
    }
    for(i=0; i<mtail; i++)
    {
        double row0;
        row0 = 0;
        pb = x;
        pa0 = a;
        a += alglib_r_block;
        for(k=0; k<n2; k++)
        {
            row0 += pb[0]*pa0[0]+pb[1]*pa0[1];            
            pa0 += 2;
            pb += 2;
        }
        if( n%2 )
            row0 += pb[0]*pa0[0];
        if( beta!=0 )
            y[0] = beta*y[0]+alpha*row0;
        else
            y[0] = alpha*row0;
        y+=stride;
    }
}
#endif


/*************************************************************************
This subroutine calculates fast MxN complex matrix-vector product:

    y := beta*y + alpha*A*x

using generic C code, where A, x, y, alpha and beta are complex.

If beta is zero, we do not use previous values of y (they are  overwritten
by alpha*A*x without ever being read). However, when  alpha  is  zero,  we 
still calculate A*x and  multiply  it  by  alpha  (this distinction can be
important when A or x contain infinities/NANs).

IMPORTANT:
* 0<=M<=alglib_c_block, 0<=N<=alglib_c_block
* A must be stored in row-major order, as sequence of double precision
  pairs. Stride is alglib_c_block (it is measured in pairs of doubles, not
  in doubles).
* Y may be referenced by cy (pointer to ae_complex) or
  dy (pointer to array of double precision pair) depending on what type of 
  output you wish. Pass pointer to Y as one of these parameters,
  AND SET OTHER PARAMETER TO NULL.
* both A and x must be aligned; y may be non-aligned.
*************************************************************************/
void _ialglib_cmv(ae_int_t m, ae_int_t n, const double *a, const double *x, ae_complex *cy, double *dy, ae_int_t stride, ae_complex alpha, ae_complex beta)
{
    ae_int_t i, j;
    const double *pa, *parow, *pb;

    parow = a;
    for(i=0; i<m; i++)
    {
        double v0 = 0, v1 = 0;
        pa = parow;
        pb = x;
        for(j=0; j<n; j++)
        {
            v0 += pa[0]*pb[0];
            v1 += pa[0]*pb[1];
            v0 -= pa[1]*pb[1];
            v1 += pa[1]*pb[0];

            pa  += 2;
            pb  += 2;
        }
        if( cy!=NULL )
        {
            double tx = (beta.x*cy->x-beta.y*cy->y)+(alpha.x*v0-alpha.y*v1);
            double ty = (beta.x*cy->y+beta.y*cy->x)+(alpha.x*v1+alpha.y*v0);
            cy->x = tx;
            cy->y = ty;
            cy+=stride;
        }
        else
        {
            double tx = (beta.x*dy[0]-beta.y*dy[1])+(alpha.x*v0-alpha.y*v1);
            double ty = (beta.x*dy[1]+beta.y*dy[0])+(alpha.x*v1+alpha.y*v0);
            dy[0] = tx;
            dy[1] = ty;
            dy += 2*stride;
        }
        parow += 2*alglib_c_block;
    }
}


/*************************************************************************
This subroutine calculates fast MxN complex matrix-vector product:

    y := beta*y + alpha*A*x

using generic C code, where A, x, y, alpha and beta are complex.

If beta is zero, we do not use previous values of y (they are  overwritten
by alpha*A*x without ever being read). However, when  alpha  is  zero,  we 
still calculate A*x and  multiply  it  by  alpha  (this distinction can be
important when A or x contain infinities/NANs).

IMPORTANT:
* 0<=M<=alglib_c_block, 0<=N<=alglib_c_block
* A must be stored in row-major order, as sequence of double precision
  pairs. Stride is alglib_c_block (it is measured in pairs of doubles, not
  in doubles).
* Y may be referenced by cy (pointer to ae_complex) or
  dy (pointer to array of double precision pair) depending on what type of 
  output you wish. Pass pointer to Y as one of these parameters,
  AND SET OTHER PARAMETER TO NULL.
* both A and x must be aligned; y may be non-aligned.

This function supports SSE2; it can be used when:
1. AE_HAS_SSE2_INTRINSICS was defined (checked at compile-time)
2. ae_cpuid() result contains CPU_SSE2 (checked at run-time)

If (1) is failed, this function will be undefined. If (2) is failed,  call 
to this function will probably crash your system. 

If  you  want  to  know  whether  it  is safe to call it, you should check 
results  of  ae_cpuid(). If CPU_SSE2 bit is set, this function is callable 
and will do its work.
*************************************************************************/
#if defined(AE_HAS_SSE2_INTRINSICS)
void _ialglib_cmv_sse2(ae_int_t m, ae_int_t n, const double *a, const double *x, ae_complex *cy, double *dy, ae_int_t stride, ae_complex alpha, ae_complex beta)
{
    ae_int_t i, j, m2;
    const double *pa0, *pa1, *parow, *pb;
    __m128d vbeta, vbetax, vbetay;
    __m128d valpha, valphax, valphay;
    
    m2 = m/2;
    parow = a;
    if( cy!=NULL )
    {
        dy = (double*)cy;
        cy = NULL;
    }
    vbeta = _mm_loadh_pd(_mm_load_sd(&beta.x),&beta.y);
    vbetax = _mm_unpacklo_pd(vbeta,vbeta);
    vbetay = _mm_unpackhi_pd(vbeta,vbeta);
    valpha = _mm_loadh_pd(_mm_load_sd(&alpha.x),&alpha.y);
    valphax = _mm_unpacklo_pd(valpha,valpha);
    valphay = _mm_unpackhi_pd(valpha,valpha);
    for(i=0; i<m2; i++)
    {
        double v0 = 0, v1 = 0, v2 = 0, v3 = 0;
        double tx, ty;
        __m128d vx, vy, vt0, vt1, vt2, vt3, vt4, vt5, vrx, vry, vtx, vty, vbeta;
        pa0 = parow;
        pa1 = parow+2*alglib_c_block;
        pb = x;
        vx = _mm_setzero_pd();
        vy = _mm_setzero_pd();
        for(j=0; j<n; j++)
        {
            vt0 = _mm_load1_pd(pb);
            vt1 = _mm_load1_pd(pb+1);
            vt2 = _mm_load_pd(pa0);
            vt3 = _mm_load_pd(pa1);
            vt5 = _mm_unpacklo_pd(vt2,vt3);
            vt4 = _mm_unpackhi_pd(vt2,vt3);
            vt2 = vt5;
            vt3 = vt4;
            
            vt2 = _mm_mul_pd(vt2,vt0);
            vx = _mm_add_pd(vx,vt2);
            vt3 = _mm_mul_pd(vt3,vt1);
            vx = _mm_sub_pd(vx,vt3);
            vt4 = _mm_mul_pd(vt4,vt0);
            vy = _mm_add_pd(vy,vt4);
            vt5 = _mm_mul_pd(vt5,vt1);
            vy = _mm_add_pd(vy,vt5);
            
            pa0 += 2;
            pa1 += 2;
            pb  += 2;
        }
        if( beta.x==0.0 && beta.y==0.0 )
        {
            vrx = _mm_setzero_pd();
            vry = _mm_setzero_pd();
        }
        else
        {
            vtx = _mm_loadh_pd(_mm_load_sd(dy+0),dy+2*stride+0);
            vty = _mm_loadh_pd(_mm_load_sd(dy+1),dy+2*stride+1);
            vrx = _mm_sub_pd(_mm_mul_pd(vbetax,vtx),_mm_mul_pd(vbetay,vty));
            vry = _mm_add_pd(_mm_mul_pd(vbetax,vty),_mm_mul_pd(vbetay,vtx));
        }
        vtx = _mm_sub_pd(_mm_mul_pd(valphax,vx),_mm_mul_pd(valphay,vy));
        vty = _mm_add_pd(_mm_mul_pd(valphax,vy),_mm_mul_pd(valphay,vx));
        vrx = _mm_add_pd(vrx,vtx);
        vry = _mm_add_pd(vry,vty);
        _mm_storel_pd(dy+0,          vrx);
        _mm_storeh_pd(dy+2*stride+0, vrx);
        _mm_storel_pd(dy+1,          vry);
        _mm_storeh_pd(dy+2*stride+1, vry);
        dy += 4*stride;        
        parow += 4*alglib_c_block;
    }
    if( m%2 )
    {
        double v0 = 0, v1 = 0, v2 = 0, v3 = 0;
        double tx, ty;
        pa0 = parow;
        pb = x;
        for(j=0; j<n; j++)
        {
            v0 += pa0[0]*pb[0];
            v1 += pa0[0]*pb[1];
            v0 -= pa0[1]*pb[1];
            v1 += pa0[1]*pb[0];

            pa0 += 2;
            pb  += 2;
        }
        if( beta.x==0.0 && beta.y==0.0 )
        {
            tx = 0.0;
            ty = 0.0;
        }
        else
        {
            tx = beta.x*dy[0]-beta.y*dy[1];
            ty = beta.x*dy[1]+beta.y*dy[0];
        }
        tx += alpha.x*v0-alpha.y*v1;
        ty += alpha.x*v1+alpha.y*v0;
        dy[0] = tx;
        dy[1] = ty;
        dy += 2*stride;
        parow += 2*alglib_c_block;
    }
}
#endif

/********************************************************************
This subroutine sets vector to zero
********************************************************************/
void _ialglib_vzero(ae_int_t n, double *p, ae_int_t stride)
{
    ae_int_t i;
    if( stride==1 )
    {
        for(i=0; i<n; i++,p++)
            *p = 0.0;
    }
    else
    {
        for(i=0; i<n; i++,p+=stride)
            *p = 0.0;
    }
}

/********************************************************************
This subroutine sets vector to zero
********************************************************************/
void _ialglib_vzero_complex(ae_int_t n, ae_complex *p, ae_int_t stride)
{
    ae_int_t i;
    if( stride==1 )
    {
        for(i=0; i<n; i++,p++)
        {
            p->x = 0.0;
            p->y = 0.0;
        }
    }
    else
    {
        for(i=0; i<n; i++,p+=stride)
        {
            p->x = 0.0;
            p->y = 0.0;
        }
    }
}


/********************************************************************
This subroutine copies unaligned real vector
********************************************************************/
void _ialglib_vcopy(ae_int_t n, const double *a, ae_int_t stridea, double *b, ae_int_t strideb)
{
    ae_int_t i, n2;
    if( stridea==1 && strideb==1 )
    {
        n2 = n/2;
        for(i=n2; i!=0; i--, a+=2, b+=2)
        {
            b[0] = a[0];
            b[1] = a[1];
        }
        if( n%2!=0 )
            b[0] = a[0];
    }
    else
    {
        for(i=0; i<n; i++,a+=stridea,b+=strideb)
            *b = *a;
    }
}


/********************************************************************
This subroutine copies unaligned complex vector
(passed as ae_complex*)

1. strideb is stride measured in complex numbers, not doubles
2. conj may be "N" (no conj.) or "C" (conj.)
********************************************************************/
void _ialglib_vcopy_complex(ae_int_t n, const ae_complex *a, ae_int_t stridea, double *b, ae_int_t strideb, const char *conj)
{
    ae_int_t i;

    /*
     * more general case
     */
    if( conj[0]=='N' || conj[0]=='n' )
    {
        for(i=0; i<n; i++,a+=stridea,b+=2*strideb)
        {
            b[0] = a->x;
            b[1] = a->y;
        }
    }
    else
    {
        for(i=0; i<n; i++,a+=stridea,b+=2*strideb)
        {
            b[0] = a->x;
            b[1] = -a->y;
        }
    }
}


/********************************************************************
This subroutine copies unaligned complex vector (passed as double*)

1. strideb is stride measured in complex numbers, not doubles
2. conj may be "N" (no conj.) or "C" (conj.)
********************************************************************/
void _ialglib_vcopy_dcomplex(ae_int_t n, const double *a, ae_int_t stridea, double *b, ae_int_t strideb, const char *conj)
{
    ae_int_t i;

    /*
     * more general case
     */
    if( conj[0]=='N' || conj[0]=='n' )
    {
        for(i=0; i<n; i++,a+=2*stridea,b+=2*strideb)
        {
            b[0] = a[0];
            b[1] = a[1];
        }
    }
    else
    {
        for(i=0; i<n; i++,a+=2*stridea,b+=2*strideb)
        {
            b[0] = a[0];
            b[1] = -a[1];
        }
    }
}


/********************************************************************
This subroutine copies matrix from  non-aligned non-contigous storage
to aligned contigous storage

A:
* MxN
* non-aligned
* non-contigous
* may be transformed during copying (as prescribed by op)

B:
* alglib_r_block*alglib_r_block (only MxN/NxM submatrix is used)
* aligned
* stride is alglib_r_block

Transformation types:
* 0 - no transform
* 1 - transposition
********************************************************************/
void _ialglib_mcopyblock(ae_int_t m, ae_int_t n, const double *a, ae_int_t op, ae_int_t stride, double *b)
{
    ae_int_t i, j, n2;
    const double *psrc;
    double *pdst;
    if( op==0 )
    {
        n2 = n/2;
        for(i=0,psrc=a; i<m; i++,a+=stride,b+=alglib_r_block,psrc=a)
        {
            for(j=0,pdst=b; j<n2; j++,pdst+=2,psrc+=2)
            {
                pdst[0] = psrc[0];
                pdst[1] = psrc[1];
            }
            if( n%2!=0 )
                pdst[0] = psrc[0];
        }
    }
    else
    {
        n2 = n/2;
        for(i=0,psrc=a; i<m; i++,a+=stride,b+=1,psrc=a)
        {
            for(j=0,pdst=b; j<n2; j++,pdst+=alglib_twice_r_block,psrc+=2)
            {
                pdst[0] = psrc[0];
                pdst[alglib_r_block] = psrc[1];
            }
            if( n%2!=0 )
                pdst[0] = psrc[0];
        }
    }
}


/********************************************************************
This subroutine copies matrix from  non-aligned non-contigous storage
to aligned contigous storage

A:
* MxN
* non-aligned
* non-contigous
* may be transformed during copying (as prescribed by op)

B:
* alglib_r_block*alglib_r_block (only MxN/NxM submatrix is used)
* aligned
* stride is alglib_r_block

Transformation types:
* 0 - no transform
* 1 - transposition

This function supports SSE2; it can be used when:
1. AE_HAS_SSE2_INTRINSICS was defined (checked at compile-time)
2. ae_cpuid() result contains CPU_SSE2 (checked at run-time)

If (1) is failed, this function will be undefined. If (2) is failed,  call 
to this function will probably crash your system. 

If  you  want  to  know  whether  it  is safe to call it, you should check 
results  of  ae_cpuid(). If CPU_SSE2 bit is set, this function is callable 
and will do its work.
********************************************************************/
#if defined(AE_HAS_SSE2_INTRINSICS)
void _ialglib_mcopyblock_sse2(ae_int_t m, ae_int_t n, const double *a, ae_int_t op, ae_int_t stride, double *b)
{
    ae_int_t i, j, nb8, mb2, ntail;
    const double *psrc0, *psrc1;
    double *pdst;
    nb8 = n/8;
    ntail = n-8*nb8;
    if( op==0 )
    {
        for(i=0,psrc0=a; i<m; i++,a+=stride,b+=alglib_r_block,psrc0=a)
        {
            pdst=b;
            for(j=0; j<nb8; j++)
            {
                __m128d v0, v1;
                v0 = _mm_loadu_pd(psrc0);
                _mm_store_pd(pdst, v0);
                v1 = _mm_loadu_pd(psrc0+2);
                _mm_store_pd(pdst+2, v1);
                v1 = _mm_loadu_pd(psrc0+4);
                _mm_store_pd(pdst+4, v1);
                v1 = _mm_loadu_pd(psrc0+6);
                _mm_store_pd(pdst+6, v1);
                pdst+=8;
                psrc0+=8;
            }
            for(j=0; j<ntail; j++)
                pdst[j] = psrc0[j];
        }
    }
    else
    {
        const double *arow0, *arow1;
        double *bcol0, *bcol1, *pdst0, *pdst1;
        ae_int_t nb4, ntail, n2;
                
        n2 = n/2;
        mb2 = m/2;
        nb4 = n/4;
        ntail = n-4*nb4;
        
        arow0 = a;
        arow1 = a+stride;
        bcol0 = b;
        bcol1 = b+1;
        for(i=0; i<mb2; i++)
        {
            psrc0 = arow0;
            psrc1 = arow1;
            pdst0 = bcol0;
            pdst1 = bcol1;
            for(j=0; j<nb4; j++)
            {
                __m128d v0, v1, v2, v3;
                v0 = _mm_loadu_pd(psrc0);
                v1 = _mm_loadu_pd(psrc1);
                v2 = _mm_loadu_pd(psrc0+2);
                v3 = _mm_loadu_pd(psrc1+2);
                _mm_store_pd(pdst0, _mm_unpacklo_pd(v0,v1));
                _mm_store_pd(pdst0+alglib_r_block, _mm_unpackhi_pd(v0,v1));                
                _mm_store_pd(pdst0+2*alglib_r_block, _mm_unpacklo_pd(v2,v3));
                _mm_store_pd(pdst0+3*alglib_r_block, _mm_unpackhi_pd(v2,v3));

                pdst0 += 4*alglib_r_block;
                pdst1 += 4*alglib_r_block;
                psrc0 += 4;
                psrc1 += 4;
            }
            for(j=0; j<ntail; j++)
            {
                pdst0[0] = psrc0[0];
                pdst1[0] = psrc1[0];
                pdst0 += alglib_r_block;
                pdst1 += alglib_r_block;
                psrc0 += 1;
                psrc1 += 1;
            }
            arow0 += 2*stride;
            arow1 += 2*stride;
            bcol0 += 2;
            bcol1 += 2;
        }
        if( m%2 )
        {
            psrc0 = arow0;
            pdst0 = bcol0;
            for(j=0; j<n2; j++)
            {
                pdst0[0] = psrc0[0];
                pdst0[alglib_r_block] = psrc0[1];
                pdst0 += alglib_twice_r_block;
                psrc0 += 2;
            }
            if( n%2!=0 )
                pdst0[0] = psrc0[0];
        }
    }
}
#endif


/********************************************************************
This subroutine copies matrix from  aligned contigous storage to non-
aligned non-contigous storage

A:
* MxN
* aligned
* contigous
* stride is alglib_r_block
* may be transformed during copying (as prescribed by op)

B:
* alglib_r_block*alglib_r_block (only MxN/NxM submatrix is used)
* non-aligned, non-contigous

Transformation types:
* 0 - no transform
* 1 - transposition
********************************************************************/
void _ialglib_mcopyunblock(ae_int_t m, ae_int_t n, const double *a, ae_int_t op, double *b, ae_int_t stride)
{
    ae_int_t i, j, n2;
    const double *psrc;
    double *pdst;
    if( op==0 )
    {
        n2 = n/2;
        for(i=0,psrc=a; i<m; i++,a+=alglib_r_block,b+=stride,psrc=a)
        {
            for(j=0,pdst=b; j<n2; j++,pdst+=2,psrc+=2)
            {
                pdst[0] = psrc[0];
                pdst[1] = psrc[1];
            }
            if( n%2!=0 )
                pdst[0] = psrc[0];
        }
    }
    else
    {
        n2 = n/2;
        for(i=0,psrc=a; i<m; i++,a++,b+=stride,psrc=a)
        {
            for(j=0,pdst=b; j<n2; j++,pdst+=2,psrc+=alglib_twice_r_block)
            {
                pdst[0] = psrc[0];
                pdst[1] = psrc[alglib_r_block];
            }
            if( n%2!=0 )
                pdst[0] = psrc[0];
        }
    }
}


/********************************************************************
This subroutine copies matrix from  non-aligned non-contigous storage
to aligned contigous storage

A:
* MxN
* non-aligned
* non-contigous
* may be transformed during copying (as prescribed by op)
* pointer to ae_complex is passed

B:
* 2*alglib_c_block*alglib_c_block doubles (only MxN/NxM submatrix is used)
* aligned
* stride is alglib_c_block
* pointer to double is passed

Transformation types:
* 0 - no transform
* 1 - transposition
* 2 - conjugate transposition
* 3 - conjugate, but no  transposition
********************************************************************/
void _ialglib_mcopyblock_complex(ae_int_t m, ae_int_t n, const ae_complex *a, ae_int_t op, ae_int_t stride, double *b)
{
    ae_int_t i, j;
    const ae_complex *psrc;
    double *pdst;
    if( op==0 )
    {
        for(i=0,psrc=a; i<m; i++,a+=stride,b+=alglib_twice_c_block,psrc=a)
            for(j=0,pdst=b; j<n; j++,pdst+=2,psrc++)
            {
                pdst[0] = psrc->x;
                pdst[1] = psrc->y;
            }
    }
    if( op==1 )
    {
        for(i=0,psrc=a; i<m; i++,a+=stride,b+=2,psrc=a)
            for(j=0,pdst=b; j<n; j++,pdst+=alglib_twice_c_block,psrc++)
            {
                pdst[0] = psrc->x;
                pdst[1] = psrc->y;
            }
    }
    if( op==2 )
    {
        for(i=0,psrc=a; i<m; i++,a+=stride,b+=2,psrc=a)
            for(j=0,pdst=b; j<n; j++,pdst+=alglib_twice_c_block,psrc++)
            {
                pdst[0] = psrc->x;
                pdst[1] = -psrc->y;
            }
    }
    if( op==3 )
    {
        for(i=0,psrc=a; i<m; i++,a+=stride,b+=alglib_twice_c_block,psrc=a)
            for(j=0,pdst=b; j<n; j++,pdst+=2,psrc++)
            {
                pdst[0] = psrc->x;
                pdst[1] = -psrc->y;
            }
    }
}


/********************************************************************
This subroutine copies matrix from aligned contigous storage to
non-aligned non-contigous storage

A:
* 2*alglib_c_block*alglib_c_block doubles (only MxN submatrix is used)
* aligned
* stride is alglib_c_block
* pointer to double is passed
* may be transformed during copying (as prescribed by op)

B:
* MxN
* non-aligned
* non-contigous
* pointer to ae_complex is passed

Transformation types:
* 0 - no transform
* 1 - transposition
* 2 - conjugate transposition
* 3 - conjugate, but no  transposition
********************************************************************/
void _ialglib_mcopyunblock_complex(ae_int_t m, ae_int_t n, const double *a, ae_int_t op, ae_complex* b, ae_int_t stride)
{
    ae_int_t i, j;
    const double *psrc;
    ae_complex *pdst;
    if( op==0 )
    {
        for(i=0,psrc=a; i<m; i++,a+=alglib_twice_c_block,b+=stride,psrc=a)
            for(j=0,pdst=b; j<n; j++,pdst++,psrc+=2)
            {
                pdst->x = psrc[0];
                pdst->y = psrc[1];
            }
    }
    if( op==1 )
    {
        for(i=0,psrc=a; i<m; i++,a+=2,b+=stride,psrc=a)
            for(j=0,pdst=b; j<n; j++,pdst++,psrc+=alglib_twice_c_block)
            {
                pdst->x = psrc[0];
                pdst->y = psrc[1];
            }
    }
    if( op==2 )
    {
        for(i=0,psrc=a; i<m; i++,a+=2,b+=stride,psrc=a)
            for(j=0,pdst=b; j<n; j++,pdst++,psrc+=alglib_twice_c_block)
            {
                pdst->x = psrc[0];
                pdst->y = -psrc[1];
            }
    }
    if( op==3 )
    {
        for(i=0,psrc=a; i<m; i++,a+=alglib_twice_c_block,b+=stride,psrc=a)
            for(j=0,pdst=b; j<n; j++,pdst++,psrc+=2)
            {
                pdst->x = psrc[0];
                pdst->y = -psrc[1];
            }
    }
}


/********************************************************************
Real GEMM kernel
********************************************************************/
ae_bool _ialglib_rmatrixgemm(ae_int_t m,
     ae_int_t n,
     ae_int_t k,
     double alpha,
     double *_a,
     ae_int_t _a_stride,
     ae_int_t optypea,
     double *_b,
     ae_int_t _b_stride,
     ae_int_t optypeb,
     double beta,
     double *_c,
     ae_int_t _c_stride)
{
    int i;
    double *crow;
    double _abuf[alglib_r_block+alglib_simd_alignment];
    double _bbuf[alglib_r_block*alglib_r_block+alglib_simd_alignment];
    double * const abuf = (double * const) ae_align(_abuf,alglib_simd_alignment);
    double * const b    = (double * const) ae_align(_bbuf,alglib_simd_alignment);
    void (*rmv)(ae_int_t, ae_int_t, const double *, const double *, double *, ae_int_t, double, double) = &_ialglib_rmv;
    void (*mcopyblock)(ae_int_t, ae_int_t, const double *, ae_int_t, ae_int_t, double *) = &_ialglib_mcopyblock;
    
    if( m>alglib_r_block || n>alglib_r_block || k>alglib_r_block || m<=0 || n<=0 || k<=0 || alpha==0.0 )
        return ae_false;

    /*
     * Check for SSE2 support
     */
#ifdef AE_HAS_SSE2_INTRINSICS
    if( ae_cpuid() & CPU_SSE2 )
    {
        rmv = &_ialglib_rmv_sse2;
        mcopyblock = &_ialglib_mcopyblock_sse2;
    }
#endif
    
    /*
     * copy b
     */
    if( optypeb==0 )
        mcopyblock(k, n, _b, 1, _b_stride, b);
    else
        mcopyblock(n, k, _b, 0, _b_stride, b);

    /*
     * multiply B by A (from the right, by rows)
     * and store result in C
     */
    crow  = _c;
    if( optypea==0 )
    {
        const double *arow = _a;
        for(i=0; i<m; i++)
        {
            _ialglib_vcopy(k, arow, 1, abuf, 1);
            if( beta==0 )
                _ialglib_vzero(n, crow, 1);
            rmv(n, k, b, abuf, crow, 1, alpha, beta);
            crow += _c_stride;
            arow += _a_stride;
        }
    }
    else
    {
        const double *acol = _a;
        for(i=0; i<m; i++)
        {
            _ialglib_vcopy(k, acol, _a_stride, abuf, 1);
            if( beta==0 )
                _ialglib_vzero(n, crow, 1);
            rmv(n, k, b, abuf, crow, 1, alpha, beta);
            crow += _c_stride;
            acol++;
        }
    }
    return ae_true;
}


/********************************************************************
Complex GEMM kernel
********************************************************************/
ae_bool _ialglib_cmatrixgemm(ae_int_t m,
     ae_int_t n,
     ae_int_t k,
     ae_complex alpha,
     ae_complex *_a,
     ae_int_t _a_stride,
     ae_int_t optypea,
     ae_complex *_b,
     ae_int_t _b_stride,
     ae_int_t optypeb,
     ae_complex beta,
     ae_complex *_c,
     ae_int_t _c_stride)
 {
    const ae_complex *arow;
    ae_complex *crow;
    ae_int_t i;
    double _loc_abuf[2*alglib_c_block+alglib_simd_alignment];
    double _loc_b[2*alglib_c_block*alglib_c_block+alglib_simd_alignment];
    double * const abuf = (double * const) ae_align(_loc_abuf,alglib_simd_alignment);
    double * const b    = (double * const) ae_align(_loc_b,   alglib_simd_alignment);
    ae_int_t brows;
    ae_int_t bcols;
    void (*cmv)(ae_int_t, ae_int_t, const double *, const double *, ae_complex *, double *, ae_int_t, ae_complex, ae_complex) = &_ialglib_cmv;
    
    if( m>alglib_c_block || n>alglib_c_block || k>alglib_c_block )
        return ae_false;

    /*
     * Check for SSE2 support
     */
#ifdef AE_HAS_SSE2_INTRINSICS
    if( ae_cpuid() & CPU_SSE2 )
    {
        cmv = &_ialglib_cmv_sse2;
    }    
#endif
    
    /*
     * copy b
     */
    brows = optypeb==0 ? k : n;
    bcols = optypeb==0 ? n : k;
    if( optypeb==0 )
        _ialglib_mcopyblock_complex(brows, bcols, _b, 1, _b_stride, b);
    if( optypeb==1 )
        _ialglib_mcopyblock_complex(brows, bcols, _b, 0, _b_stride, b);
    if( optypeb==2 )
        _ialglib_mcopyblock_complex(brows, bcols, _b, 3, _b_stride, b);

    /*
     * multiply B by A (from the right, by rows)
     * and store result in C
     */
    arow  = _a;
    crow  = _c;
    for(i=0; i<m; i++)
    {
        if( optypea==0 )
        {
            _ialglib_vcopy_complex(k, arow, 1, abuf, 1, "No conj");
            arow += _a_stride;
        }
        else if( optypea==1 )
        {
            _ialglib_vcopy_complex(k, arow, _a_stride, abuf, 1, "No conj");
            arow++;
        }
        else
        {
            _ialglib_vcopy_complex(k, arow, _a_stride, abuf, 1, "Conj");
            arow++;
        }
        if( beta.x==0 && beta.y==0 )
            _ialglib_vzero_complex(n, crow, 1);
        cmv(n, k, b, abuf, crow, NULL, 1, alpha, beta);
        crow += _c_stride;
    }
    return ae_true;
}


/********************************************************************
complex TRSM kernel
********************************************************************/
ae_bool _ialglib_cmatrixrighttrsm(ae_int_t m,
     ae_int_t n,
     ae_complex *_a,
     ae_int_t _a_stride,
     ae_bool isupper,
     ae_bool isunit,
     ae_int_t optype,
     ae_complex *_x,
     ae_int_t _x_stride)
{
    /*
     * local buffers
     */
    double *pdiag;
    ae_int_t i;
    double _loc_abuf[2*alglib_c_block*alglib_c_block+alglib_simd_alignment];
    double _loc_xbuf[2*alglib_c_block*alglib_c_block+alglib_simd_alignment];
    double _loc_tmpbuf[2*alglib_c_block+alglib_simd_alignment];
    double * const abuf   = (double * const) ae_align(_loc_abuf,  alglib_simd_alignment);
    double * const xbuf   = (double * const) ae_align(_loc_xbuf,  alglib_simd_alignment);
    double * const tmpbuf = (double * const) ae_align(_loc_tmpbuf,alglib_simd_alignment);
    ae_bool uppera;
    void (*cmv)(ae_int_t, ae_int_t, const double *, const double *, ae_complex *, double *, ae_int_t, ae_complex, ae_complex) = &_ialglib_cmv;
    
    if( m>alglib_c_block || n>alglib_c_block )
        return ae_false;

    /*
     * Check for SSE2 support
     */
#ifdef AE_HAS_SSE2_INTRINSICS
    if( ae_cpuid() & CPU_SSE2 )
    {
        cmv = &_ialglib_cmv_sse2;
    }    
#endif
    
    /*
     * Prepare
     */
    _ialglib_mcopyblock_complex(n, n, _a, optype, _a_stride, abuf);
    _ialglib_mcopyblock_complex(m, n, _x, 0, _x_stride, xbuf);
    if( isunit )
        for(i=0,pdiag=abuf; i<n; i++,pdiag+=2*(alglib_c_block+1))
        {
            pdiag[0] = 1.0;
            pdiag[1] = 0.0;
        }
    if( optype==0 )
        uppera = isupper;
    else
        uppera = !isupper;

    /*
     * Solve Y*A^-1=X where A is upper or lower triangular
     */
    if( uppera )
    {
        for(i=0,pdiag=abuf; i<n; i++,pdiag+=2*(alglib_c_block+1))
        {
            ae_complex tmp_c;
            ae_complex beta;
            ae_complex alpha;
            tmp_c.x = pdiag[0];
            tmp_c.y = pdiag[1];
            beta = ae_c_d_div(1.0, tmp_c);
            alpha.x = -beta.x;
            alpha.y = -beta.y;
            _ialglib_vcopy_dcomplex(i, abuf+2*i, alglib_c_block, tmpbuf, 1, "No conj");
            cmv(m, i, xbuf, tmpbuf, NULL, xbuf+2*i, alglib_c_block, alpha, beta);
        }
        _ialglib_mcopyunblock_complex(m, n, xbuf, 0, _x, _x_stride);
    }
    else
    {
        for(i=n-1,pdiag=abuf+2*((n-1)*alglib_c_block+(n-1)); i>=0; i--,pdiag-=2*(alglib_c_block+1))
        {
            ae_complex tmp_c;
            ae_complex beta;
            ae_complex alpha;
            tmp_c.x = pdiag[0];
            tmp_c.y = pdiag[1];
            beta = ae_c_d_div(1.0, tmp_c);
            alpha.x = -beta.x;
            alpha.y = -beta.y;
            _ialglib_vcopy_dcomplex(n-1-i, pdiag+2*alglib_c_block, alglib_c_block, tmpbuf, 1, "No conj");
            cmv(m, n-1-i, xbuf+2*(i+1), tmpbuf, NULL, xbuf+2*i, alglib_c_block, alpha, beta);
        }
        _ialglib_mcopyunblock_complex(m, n, xbuf, 0, _x, _x_stride);
    }
    return ae_true;
}


/********************************************************************
real TRSM kernel
********************************************************************/
ae_bool _ialglib_rmatrixrighttrsm(ae_int_t m,
     ae_int_t n,
     double *_a,
     ae_int_t _a_stride,
     ae_bool isupper,
     ae_bool isunit,
     ae_int_t optype,
     double *_x,
     ae_int_t _x_stride)
{
    /*
     * local buffers
     */
    double *pdiag;
    ae_int_t i;
    double _loc_abuf[alglib_r_block*alglib_r_block+alglib_simd_alignment];
    double _loc_xbuf[alglib_r_block*alglib_r_block+alglib_simd_alignment];
    double _loc_tmpbuf[alglib_r_block+alglib_simd_alignment];
    double * const abuf   = (double * const) ae_align(_loc_abuf,  alglib_simd_alignment);
    double * const xbuf   = (double * const) ae_align(_loc_xbuf,  alglib_simd_alignment);
    double * const tmpbuf = (double * const) ae_align(_loc_tmpbuf,alglib_simd_alignment);
    ae_bool uppera;
    void (*rmv)(ae_int_t, ae_int_t, const double *, const double *, double *, ae_int_t, double, double) = &_ialglib_rmv;
    void (*mcopyblock)(ae_int_t, ae_int_t, const double *, ae_int_t, ae_int_t, double *) = &_ialglib_mcopyblock;
    
    if( m>alglib_r_block || n>alglib_r_block )
        return ae_false;

    /*
     * Check for SSE2 support
     */
#ifdef AE_HAS_SSE2_INTRINSICS
    if( ae_cpuid() & CPU_SSE2 )
    {
        rmv = &_ialglib_rmv_sse2;
        mcopyblock = &_ialglib_mcopyblock_sse2;
    }    
#endif
    
    /*
     * Prepare
     */
    mcopyblock(n, n, _a, optype, _a_stride, abuf);
    mcopyblock(m, n, _x, 0, _x_stride, xbuf);
    if( isunit )
        for(i=0,pdiag=abuf; i<n; i++,pdiag+=alglib_r_block+1)
            *pdiag = 1.0;
    if( optype==0 )
        uppera = isupper;
    else
        uppera = !isupper;

    /*
     * Solve Y*A^-1=X where A is upper or lower triangular
     */
    if( uppera )
    {
        for(i=0,pdiag=abuf; i<n; i++,pdiag+=alglib_r_block+1)
        {
            double beta  = 1.0/(*pdiag);
            double alpha = -beta;
            _ialglib_vcopy(i, abuf+i, alglib_r_block, tmpbuf, 1);
            rmv(m, i, xbuf, tmpbuf, xbuf+i, alglib_r_block, alpha, beta);
        }
        _ialglib_mcopyunblock(m, n, xbuf, 0, _x, _x_stride);
    }
    else
    {
        for(i=n-1,pdiag=abuf+(n-1)*alglib_r_block+(n-1); i>=0; i--,pdiag-=alglib_r_block+1)
        {
            double beta = 1.0/(*pdiag);
            double alpha = -beta;
            _ialglib_vcopy(n-1-i, pdiag+alglib_r_block, alglib_r_block, tmpbuf+i+1, 1);
            rmv(m, n-1-i, xbuf+i+1, tmpbuf+i+1, xbuf+i, alglib_r_block, alpha, beta);
        }
        _ialglib_mcopyunblock(m, n, xbuf, 0, _x, _x_stride);
    }
    return ae_true;
}


/********************************************************************
complex TRSM kernel
********************************************************************/
ae_bool _ialglib_cmatrixlefttrsm(ae_int_t m,
     ae_int_t n,
     ae_complex *_a,
     ae_int_t _a_stride,
     ae_bool isupper,
     ae_bool isunit,
     ae_int_t optype,
     ae_complex *_x,
     ae_int_t _x_stride)
{
    /*
     * local buffers
     */
    double *pdiag, *arow;
    ae_int_t i;
    double _loc_abuf[2*alglib_c_block*alglib_c_block+alglib_simd_alignment];
    double _loc_xbuf[2*alglib_c_block*alglib_c_block+alglib_simd_alignment];
    double _loc_tmpbuf[2*alglib_c_block+alglib_simd_alignment];
    double * const abuf   = (double * const) ae_align(_loc_abuf,  alglib_simd_alignment);
    double * const xbuf   = (double * const) ae_align(_loc_xbuf,  alglib_simd_alignment);
    double * const tmpbuf = (double * const) ae_align(_loc_tmpbuf,alglib_simd_alignment);
    ae_bool uppera;
    void (*cmv)(ae_int_t, ae_int_t, const double *, const double *, ae_complex *, double *, ae_int_t, ae_complex, ae_complex) = &_ialglib_cmv;
    
    if( m>alglib_c_block || n>alglib_c_block )
        return ae_false;

    /*
     * Check for SSE2 support
     */
#ifdef AE_HAS_SSE2_INTRINSICS
    if( ae_cpuid() & CPU_SSE2 )
    {
        cmv = &_ialglib_cmv_sse2;
    }    
#endif
    
    /*
     * Prepare
     * Transpose X (so we may use mv, which calculates A*x, but not x*A)
     */
    _ialglib_mcopyblock_complex(m, m, _a, optype, _a_stride, abuf);
    _ialglib_mcopyblock_complex(m, n, _x, 1, _x_stride, xbuf);
    if( isunit )
        for(i=0,pdiag=abuf; i<m; i++,pdiag+=2*(alglib_c_block+1))
        {
            pdiag[0] = 1.0;
            pdiag[1] = 0.0;
        }
    if( optype==0 )
        uppera = isupper;
    else
        uppera = !isupper;

    /*
     * Solve A^-1*Y^T=X^T where A is upper or lower triangular
     */
    if( uppera )
    {
        for(i=m-1,pdiag=abuf+2*((m-1)*alglib_c_block+(m-1)); i>=0; i--,pdiag-=2*(alglib_c_block+1))
        {
            ae_complex tmp_c;
            ae_complex beta;
            ae_complex alpha;
            tmp_c.x = pdiag[0];
            tmp_c.y = pdiag[1];
            beta = ae_c_d_div(1.0, tmp_c);
            alpha.x = -beta.x;
            alpha.y = -beta.y;
            _ialglib_vcopy_dcomplex(m-1-i, pdiag+2, 1, tmpbuf, 1, "No conj");
            cmv(n, m-1-i, xbuf+2*(i+1), tmpbuf, NULL, xbuf+2*i, alglib_c_block, alpha, beta);
        }
        _ialglib_mcopyunblock_complex(m, n, xbuf, 1, _x, _x_stride);
    }
    else
    {   for(i=0,pdiag=abuf,arow=abuf; i<m; i++,pdiag+=2*(alglib_c_block+1),arow+=2*alglib_c_block)
        {
            ae_complex tmp_c;
            ae_complex beta;
            ae_complex alpha;
            tmp_c.x = pdiag[0];
            tmp_c.y = pdiag[1];
            beta = ae_c_d_div(1.0, tmp_c);
            alpha.x = -beta.x;
            alpha.y = -beta.y;
            _ialglib_vcopy_dcomplex(i, arow, 1, tmpbuf, 1, "No conj");
            cmv(n, i, xbuf, tmpbuf, NULL, xbuf+2*i, alglib_c_block, alpha, beta);
        }
        _ialglib_mcopyunblock_complex(m, n, xbuf, 1, _x, _x_stride);
    }
    return ae_true;
}


/********************************************************************
real TRSM kernel
********************************************************************/
ae_bool _ialglib_rmatrixlefttrsm(ae_int_t m,
     ae_int_t n,
     double *_a,
     ae_int_t _a_stride,
     ae_bool isupper,
     ae_bool isunit,
     ae_int_t optype,
     double *_x,
     ae_int_t _x_stride)
{
    /*
     * local buffers
     */
    double *pdiag, *arow;
    ae_int_t i;
    double _loc_abuf[alglib_r_block*alglib_r_block+alglib_simd_alignment];
    double _loc_xbuf[alglib_r_block*alglib_r_block+alglib_simd_alignment];
    double _loc_tmpbuf[alglib_r_block+alglib_simd_alignment];
    double * const abuf   = (double * const) ae_align(_loc_abuf,  alglib_simd_alignment);
    double * const xbuf   = (double * const) ae_align(_loc_xbuf,  alglib_simd_alignment);
    double * const tmpbuf = (double * const) ae_align(_loc_tmpbuf,alglib_simd_alignment);
    ae_bool uppera;
    void (*rmv)(ae_int_t, ae_int_t, const double *, const double *, double *, ae_int_t, double, double) = &_ialglib_rmv;
    void (*mcopyblock)(ae_int_t, ae_int_t, const double *, ae_int_t, ae_int_t, double *) = &_ialglib_mcopyblock;
    
    if( m>alglib_r_block || n>alglib_r_block )
        return ae_false;

    /*
     * Check for SSE2 support
     */
#ifdef AE_HAS_SSE2_INTRINSICS
    if( ae_cpuid() & CPU_SSE2 )
    {
        rmv = &_ialglib_rmv_sse2;
        mcopyblock = &_ialglib_mcopyblock_sse2;
    }    
#endif
    
    /*
     * Prepare
     * Transpose X (so we may use mv, which calculates A*x, but not x*A)
     */
    mcopyblock(m, m, _a, optype, _a_stride, abuf);
    mcopyblock(m, n, _x, 1, _x_stride, xbuf);
    if( isunit )
        for(i=0,pdiag=abuf; i<m; i++,pdiag+=alglib_r_block+1)
            *pdiag = 1.0;
    if( optype==0 )
        uppera = isupper;
    else
        uppera = !isupper;

    /*
     * Solve A^-1*Y^T=X^T where A is upper or lower triangular
     */
    if( uppera )
    {
        for(i=m-1,pdiag=abuf+(m-1)*alglib_r_block+(m-1); i>=0; i--,pdiag-=alglib_r_block+1)
        {
            double beta = 1.0/(*pdiag);
            double alpha = -beta;
            _ialglib_vcopy(m-1-i, pdiag+1, 1, tmpbuf+i+1, 1);
            rmv(n, m-1-i, xbuf+i+1, tmpbuf+i+1, xbuf+i, alglib_r_block, alpha, beta);
        }
        _ialglib_mcopyunblock(m, n, xbuf, 1, _x, _x_stride);
    }
    else
    {   for(i=0,pdiag=abuf,arow=abuf; i<m; i++,pdiag+=alglib_r_block+1,arow+=alglib_r_block)
        {
            double beta = 1.0/(*pdiag);
            double alpha = -beta;
            _ialglib_vcopy(i, arow, 1, tmpbuf, 1);
            rmv(n, i, xbuf, tmpbuf, xbuf+i, alglib_r_block, alpha, beta);
        }
        _ialglib_mcopyunblock(m, n, xbuf, 1, _x, _x_stride);
    }
    return ae_true;
}


/********************************************************************
complex SYRK kernel
********************************************************************/
ae_bool _ialglib_cmatrixsyrk(ae_int_t n,
     ae_int_t k,
     double alpha,
     ae_complex *_a,
     ae_int_t _a_stride,
     ae_int_t optypea,
     double beta,
     ae_complex *_c,
     ae_int_t _c_stride,
     ae_bool isupper)
{
    /*
     * local buffers
     */
    double *arow, *crow;
    ae_complex c_alpha, c_beta;
    ae_int_t i;
    double _loc_abuf[2*alglib_c_block*alglib_c_block+alglib_simd_alignment];
    double _loc_cbuf[2*alglib_c_block*alglib_c_block+alglib_simd_alignment];
    double _loc_tmpbuf[2*alglib_c_block+alglib_simd_alignment];
    double * const abuf   = (double * const) ae_align(_loc_abuf,  alglib_simd_alignment);
    double * const cbuf   = (double * const) ae_align(_loc_cbuf,  alglib_simd_alignment);
    double * const tmpbuf = (double * const) ae_align(_loc_tmpbuf,alglib_simd_alignment);

    if( n>alglib_c_block || k>alglib_c_block )
        return ae_false;
    if( n==0 )
        return ae_true;

    /*
     * copy A and C, task is transformed to "A*A^H"-form.
     * if beta==0, then C is filled by zeros (and not referenced)
     *
     * alpha==0 or k==0 are correctly processed (A is not referenced)
     */
    c_alpha.x = alpha;
    c_alpha.y = 0;
    c_beta.x = beta;
    c_beta.y = 0;
    if( alpha==0 )
        k = 0;
    if( k>0 )
    {
        if( optypea==0 )
            _ialglib_mcopyblock_complex(n, k, _a, 3, _a_stride, abuf);
        else
            _ialglib_mcopyblock_complex(k, n, _a, 1, _a_stride, abuf);
    }
    _ialglib_mcopyblock_complex(n, n, _c, 0, _c_stride, cbuf);
    if( beta==0 )
    {
        for(i=0,crow=cbuf; i<n; i++,crow+=2*alglib_c_block)
            if( isupper )
                _ialglib_vzero(2*(n-i), crow+2*i, 1);
            else
                _ialglib_vzero(2*(i+1), crow, 1);
    }


    /*
     * update C
     */
    if( isupper )
    {
        for(i=0,arow=abuf,crow=cbuf; i<n; i++,arow+=2*alglib_c_block,crow+=2*alglib_c_block)
        {
            _ialglib_vcopy_dcomplex(k, arow, 1, tmpbuf, 1, "Conj");
            _ialglib_cmv(n-i, k, arow, tmpbuf, NULL, crow+2*i, 1, c_alpha, c_beta);
        }
    }
    else
    {
        for(i=0,arow=abuf,crow=cbuf; i<n; i++,arow+=2*alglib_c_block,crow+=2*alglib_c_block)
        {
            _ialglib_vcopy_dcomplex(k, arow, 1, tmpbuf, 1, "Conj");
            _ialglib_cmv(i+1, k, abuf, tmpbuf, NULL, crow, 1, c_alpha, c_beta);
        }
    }

    /*
     * copy back
     */
    _ialglib_mcopyunblock_complex(n, n, cbuf, 0, _c, _c_stride);

    return ae_true;
}


/********************************************************************
real SYRK kernel
********************************************************************/
ae_bool _ialglib_rmatrixsyrk(ae_int_t n,
     ae_int_t k,
     double alpha,
     double *_a,
     ae_int_t _a_stride,
     ae_int_t optypea,
     double beta,
     double *_c,
     ae_int_t _c_stride,
     ae_bool isupper)
{
    /*
     * local buffers
     */
    double *arow, *crow;
    ae_int_t i;
    double _loc_abuf[alglib_r_block*alglib_r_block+alglib_simd_alignment];
    double _loc_cbuf[alglib_r_block*alglib_r_block+alglib_simd_alignment];
    double * const abuf   = (double * const) ae_align(_loc_abuf,  alglib_simd_alignment);
    double * const cbuf   = (double * const) ae_align(_loc_cbuf,  alglib_simd_alignment);

    if( n>alglib_r_block || k>alglib_r_block )
        return ae_false;
    if( n==0 )
        return ae_true;

    /*
     * copy A and C, task is transformed to "A*A^T"-form.
     * if beta==0, then C is filled by zeros (and not referenced)
     *
     * alpha==0 or k==0 are correctly processed (A is not referenced)
     */
    if( alpha==0 )
        k = 0;
    if( k>0 )
    {
        if( optypea==0 )
            _ialglib_mcopyblock(n, k, _a, 0, _a_stride, abuf);
        else
            _ialglib_mcopyblock(k, n, _a, 1, _a_stride, abuf);
    }
    _ialglib_mcopyblock(n, n, _c, 0, _c_stride, cbuf);
    if( beta==0 )
    {
        for(i=0,crow=cbuf; i<n; i++,crow+=alglib_r_block)
            if( isupper )
                _ialglib_vzero(n-i, crow+i, 1);
            else
                _ialglib_vzero(i+1, crow, 1);
    }


    /*
     * update C
     */
    if( isupper )
    {
        for(i=0,arow=abuf,crow=cbuf; i<n; i++,arow+=alglib_r_block,crow+=alglib_r_block)
        {
            _ialglib_rmv(n-i, k, arow, arow, crow+i, 1, alpha, beta);
        }
    }
    else
    {
        for(i=0,arow=abuf,crow=cbuf; i<n; i++,arow+=alglib_r_block,crow+=alglib_r_block)
        {
            _ialglib_rmv(i+1, k, abuf, arow, crow, 1, alpha, beta);
        }
    }

    /*
     * copy back
     */
    _ialglib_mcopyunblock(n, n, cbuf, 0, _c, _c_stride);

    return ae_true;
}


/********************************************************************
complex rank-1 kernel
********************************************************************/
ae_bool _ialglib_cmatrixrank1(ae_int_t m,
     ae_int_t n,
     ae_complex *_a,
     ae_int_t _a_stride,
     ae_complex *_u,
     ae_complex *_v)
{
    ae_complex *arow, *pu, *pv, *vtmp, *dst;
    ae_int_t n2 = n/2;
    ae_int_t i, j;

    /*
     * update pairs of rows
     */
    arow  = _a;
    pu    = _u;
    vtmp  = _v;
    for(i=0; i<m; i++, arow+=_a_stride, pu++)
    {
        /*
         * update by two
         */
        for(j=0,pv=vtmp, dst=arow; j<n2; j++, dst+=2, pv+=2)
        {
            double ux  = pu[0].x;
            double uy  = pu[0].y;
            double v0x = pv[0].x;
            double v0y = pv[0].y;
            double v1x = pv[1].x;
            double v1y = pv[1].y;
            dst[0].x += ux*v0x-uy*v0y;
            dst[0].y += ux*v0y+uy*v0x;
            dst[1].x += ux*v1x-uy*v1y;
            dst[1].y += ux*v1y+uy*v1x;
        }

        /*
         * final update
         */
        if( n%2!=0 )
        {
            double ux = pu[0].x;
            double uy = pu[0].y;
            double vx = pv[0].x;
            double vy = pv[0].y;
            dst[0].x += ux*vx-uy*vy;
            dst[0].y += ux*vy+uy*vx;
        }
    }
    return ae_true;
}


/********************************************************************
real rank-1 kernel
********************************************************************/
ae_bool _ialglib_rmatrixrank1(ae_int_t m,
     ae_int_t n,
     double *_a,
     ae_int_t _a_stride,
     double *_u,
     double *_v)
{
    double *arow0, *arow1, *pu, *pv, *vtmp, *dst0, *dst1;
    ae_int_t m2 = m/2;
    ae_int_t n2 = n/2;
    ae_int_t stride  = _a_stride;
    ae_int_t stride2 = 2*_a_stride;
    ae_int_t i, j;

    /*
     * update pairs of rows
     */
    arow0 = _a;
    arow1 = arow0+stride;
    pu    = _u;
    vtmp  = _v;
    for(i=0; i<m2; i++,arow0+=stride2,arow1+=stride2,pu+=2)
    {
        /*
         * update by two
         */
        for(j=0,pv=vtmp, dst0=arow0, dst1=arow1; j<n2; j++, dst0+=2, dst1+=2, pv+=2)
        {
            dst0[0] += pu[0]*pv[0];
            dst0[1] += pu[0]*pv[1];
            dst1[0] += pu[1]*pv[0];
            dst1[1] += pu[1]*pv[1];
        }

        /*
         * final update
         */
        if( n%2!=0 )
        {
            dst0[0] += pu[0]*pv[0];
            dst1[0] += pu[1]*pv[0];
        }
    }

    /*
     * update last row
     */
    if( m%2!=0 )
    {
        /*
         * update by two
         */
        for(j=0,pv=vtmp, dst0=arow0; j<n2; j++, dst0+=2, pv+=2)
        {
            dst0[0] += pu[0]*pv[0];
            dst0[1] += pu[0]*pv[1];
        }

        /*
         * final update
         */
        if( n%2!=0 )
            dst0[0] += pu[0]*pv[0];
    }
    return ae_true;
}


/********************************************************************
Interface functions for efficient kernels
********************************************************************/
ae_bool _ialglib_i_rmatrixgemmf(ae_int_t m,
     ae_int_t n,
     ae_int_t k,
     double alpha,
     ae_matrix *_a,
     ae_int_t ia,
     ae_int_t ja,
     ae_int_t optypea,
     ae_matrix *_b,
     ae_int_t ib,
     ae_int_t jb,
     ae_int_t optypeb,
     double beta,
     ae_matrix *_c,
     ae_int_t ic,
     ae_int_t jc)
{
    return _ialglib_rmatrixgemm(m, n, k, alpha, _a->ptr.pp_double[ia]+ja, _a->stride, optypea, _b->ptr.pp_double[ib]+jb, _b->stride, optypeb, beta, _c->ptr.pp_double[ic]+jc, _c->stride);
}

ae_bool _ialglib_i_cmatrixgemmf(ae_int_t m,
     ae_int_t n,
     ae_int_t k,
     ae_complex alpha,
     ae_matrix *_a,
     ae_int_t ia,
     ae_int_t ja,
     ae_int_t optypea,
     ae_matrix *_b,
     ae_int_t ib,
     ae_int_t jb,
     ae_int_t optypeb,
     ae_complex beta,
     ae_matrix *_c,
     ae_int_t ic,
     ae_int_t jc)
{
    return _ialglib_cmatrixgemm(m, n, k, alpha, _a->ptr.pp_complex[ia]+ja, _a->stride, optypea, _b->ptr.pp_complex[ib]+jb, _b->stride, optypeb, beta, _c->ptr.pp_complex[ic]+jc, _c->stride);
}

ae_bool _ialglib_i_cmatrixrighttrsmf(ae_int_t m,
     ae_int_t n,
     ae_matrix *a,
     ae_int_t i1,
     ae_int_t j1,
     ae_bool isupper,
     ae_bool isunit,
     ae_int_t optype,
     ae_matrix *x,
     ae_int_t i2,
     ae_int_t j2)
{
    return _ialglib_cmatrixrighttrsm(m, n, &a->ptr.pp_complex[i1][j1], a->stride, isupper, isunit, optype, &x->ptr.pp_complex[i2][j2], x->stride);
}

ae_bool _ialglib_i_rmatrixrighttrsmf(ae_int_t m,
     ae_int_t n,
     ae_matrix *a,
     ae_int_t i1,
     ae_int_t j1,
     ae_bool isupper,
     ae_bool isunit,
     ae_int_t optype,
     ae_matrix *x,
     ae_int_t i2,
     ae_int_t j2)
{
    return _ialglib_rmatrixrighttrsm(m, n, &a->ptr.pp_double[i1][j1], a->stride, isupper, isunit, optype, &x->ptr.pp_double[i2][j2], x->stride);
}

ae_bool _ialglib_i_cmatrixlefttrsmf(ae_int_t m,
     ae_int_t n,
     ae_matrix *a,
     ae_int_t i1,
     ae_int_t j1,
     ae_bool isupper,
     ae_bool isunit,
     ae_int_t optype,
     ae_matrix *x,
     ae_int_t i2,
     ae_int_t j2)
{
    return _ialglib_cmatrixlefttrsm(m, n, &a->ptr.pp_complex[i1][j1], a->stride, isupper, isunit, optype, &x->ptr.pp_complex[i2][j2], x->stride);
}

ae_bool _ialglib_i_rmatrixlefttrsmf(ae_int_t m,
     ae_int_t n,
     ae_matrix *a,
     ae_int_t i1,
     ae_int_t j1,
     ae_bool isupper,
     ae_bool isunit,
     ae_int_t optype,
     ae_matrix *x,
     ae_int_t i2,
     ae_int_t j2)
{
    return _ialglib_rmatrixlefttrsm(m, n, &a->ptr.pp_double[i1][j1], a->stride, isupper, isunit, optype, &x->ptr.pp_double[i2][j2], x->stride);
}

ae_bool _ialglib_i_cmatrixsyrkf(ae_int_t n,
     ae_int_t k,
     double alpha,
     ae_matrix *a,
     ae_int_t ia,
     ae_int_t ja,
     ae_int_t optypea,
     double beta,
     ae_matrix *c,
     ae_int_t ic,
     ae_int_t jc,
     ae_bool isupper)
{
    return _ialglib_cmatrixsyrk(n, k, alpha, &a->ptr.pp_complex[ia][ja], a->stride, optypea, beta, &c->ptr.pp_complex[ic][jc], c->stride, isupper);
}

ae_bool _ialglib_i_rmatrixsyrkf(ae_int_t n,
     ae_int_t k,
     double alpha,
     ae_matrix *a,
     ae_int_t ia,
     ae_int_t ja,
     ae_int_t optypea,
     double beta,
     ae_matrix *c,
     ae_int_t ic,
     ae_int_t jc,
     ae_bool isupper)
{
    return _ialglib_rmatrixsyrk(n, k, alpha, &a->ptr.pp_double[ia][ja], a->stride, optypea, beta, &c->ptr.pp_double[ic][jc], c->stride, isupper);
}

ae_bool _ialglib_i_cmatrixrank1f(ae_int_t m,
     ae_int_t n,
     ae_matrix *a,
     ae_int_t ia,
     ae_int_t ja,
     ae_vector *u,
     ae_int_t uoffs,
     ae_vector *v,
     ae_int_t voffs)
{
    return _ialglib_cmatrixrank1(m, n, &a->ptr.pp_complex[ia][ja], a->stride, &u->ptr.p_complex[uoffs], &v->ptr.p_complex[voffs]);
}

ae_bool _ialglib_i_rmatrixrank1f(ae_int_t m,
     ae_int_t n,
     ae_matrix *a,
     ae_int_t ia,
     ae_int_t ja,
     ae_vector *u,
     ae_int_t uoffs,
     ae_vector *v,
     ae_int_t voffs)
{
    return _ialglib_rmatrixrank1(m, n, &a->ptr.pp_double[ia][ja], a->stride, &u->ptr.p_double[uoffs], &v->ptr.p_double[voffs]);
}




/********************************************************************
This function reads rectangular matrix A given by two column pointers
col0 and col1 and stride src_stride and moves it into contiguous row-
by-row storage given by dst.

It can handle following special cases:
* col1==NULL    in this case second column of A is filled by zeros
********************************************************************/
void _ialglib_pack_n2(
    double *col0,
    double *col1,
    ae_int_t n,
    ae_int_t src_stride,
    double *dst)
{
    ae_int_t n2, j, stride2;
    
    /*
     * handle special case
     */
    if( col1==NULL )
    {
        for(j=0; j<n; j++)
        {
            dst[0] = *col0;
            dst[1] = 0.0;
            col0 += src_stride;
            dst  += 2;
        }
        return;
    }

    /*
     * handle general case
     */
    n2 = n/2;
    stride2 = src_stride*2;
    for(j=0; j<n2; j++)
    {
        dst[0] = *col0;
        dst[1] = *col1;
        dst[2] = col0[src_stride];
        dst[3] = col1[src_stride];
        col0 += stride2;
        col1 += stride2;
        dst  += 4;
    }
    if( n%2 )
    {
        dst[0] = *col0;
        dst[1] = *col1;
    }
}

/*************************************************************************
This function reads rectangular matrix A given by two column pointers col0 
and  col1  and  stride src_stride and moves it into  contiguous row-by-row 
storage given by dst.

dst must be aligned, col0 and col1 may be non-aligned.

It can handle following special cases:
* col1==NULL        in this case second column of A is filled by zeros
* src_stride==1     efficient SSE-based code is used
* col1-col0==1      efficient SSE-based code is used

This function supports SSE2; it can be used when:
1. AE_HAS_SSE2_INTRINSICS was defined (checked at compile-time)
2. ae_cpuid() result contains CPU_SSE2 (checked at run-time)

If  you  want  to  know  whether  it  is safe to call it, you should check 
results  of  ae_cpuid(). If CPU_SSE2 bit is set, this function is callable 
and will do its work.
*************************************************************************/
#if defined(AE_HAS_SSE2_INTRINSICS)
void _ialglib_pack_n2_sse2(
    double *col0,
    double *col1,
    ae_int_t n,
    ae_int_t src_stride,
    double *dst)
{
    ae_int_t n2, j, stride2;
    
    /*
     * handle special case: col1==NULL
     */
    if( col1==NULL )
    {
        for(j=0; j<n; j++)
        {
            dst[0] = *col0;
            dst[1] = 0.0;
            col0 += src_stride;
            dst  += 2;
        }
        return;
    }

    /*
     * handle unit stride
     */
    if( src_stride==1 )
    {
        __m128d v0, v1, r0, r1;
        n2 = n/2;
        for(j=0; j<n2; j++)
        {
            v0 = _mm_loadu_pd(col0);
            col0 += 2;
            v1 = _mm_loadu_pd(col1);
            col1 += 2;
            _mm_store_pd(dst,  _mm_unpacklo_pd(v0,v1));
            _mm_store_pd(dst+2,_mm_unpackhi_pd(v0,v1));
            dst  += 4;
        }
        if( n%2 )
        {
            dst[0] = *col0;
            dst[1] = *col1;
        }
        return;
    }

    /*
     * handle col1-col0==1
     */
    if( col1-col0==1 )
    {
        __m128d v0, v1;
        n2 = n/2;
        stride2 = 2*src_stride;
        for(j=0; j<n2; j++)
        {
            v0 = _mm_loadu_pd(col0);
            v1 = _mm_loadu_pd(col0+src_stride);
            _mm_store_pd(dst,  v0);
            _mm_store_pd(dst+2,v1);
            col0 += stride2;
            dst  += 4;
        }
        if( n%2 )
        {
            dst[0] = col0[0];
            dst[1] = col0[1];
        }
        return;
    }
    
    /*
     * handle general case
     */
    n2 = n/2;
    stride2 = src_stride*2;
    for(j=0; j<n2; j++)
    {
        dst[0] = *col0;
        dst[1] = *col1;
        dst[2] = col0[src_stride];
        dst[3] = col1[src_stride];
        col0 += stride2;
        col1 += stride2;
        dst  += 4;
    }
    if( n%2 )
    {
        dst[0] = *col0;
        dst[1] = *col1;
    }
}
#endif


/********************************************************************
This function calculates R := alpha*A'*B+beta*R where A and B are Kx2 
matrices stored in contiguous row-by-row storage,  R  is  2x2  matrix
stored in non-contiguous row-by-row storage.

A and B must be aligned; R may be non-aligned.

If beta is zero, contents of R is ignored (not  multiplied  by zero -
just ignored).

However, when alpha is zero, we still calculate A'*B, which is 
multiplied by zero afterwards.

Function accepts additional parameter store_mode:
* if 0, full R is stored
* if 1, only first row of R is stored
* if 2, only first column of R is stored
* if 3, only top left element of R is stored
********************************************************************/
void _ialglib_mm22(double alpha, const double *a, const double *b, ae_int_t k, double beta, double *r, ae_int_t stride, ae_int_t store_mode)
{
    double v00, v01, v10, v11;
    ae_int_t t;
    v00 = 0.0;
    v01 = 0.0;
    v10 = 0.0;
    v11 = 0.0;
    for(t=0; t<k; t++)
    {
        v00 += a[0]*b[0];
        v01 += a[0]*b[1];
        v10 += a[1]*b[0];
        v11 += a[1]*b[1];
        a+=2;
        b+=2;
    }
    if( store_mode==0 )
    {
        if( beta==0 )
        {
            r[0] = alpha*v00;
            r[1] = alpha*v01;
            r[stride+0] = alpha*v10;
            r[stride+1] = alpha*v11;
        }
        else
        {
            r[0] = beta*r[0] + alpha*v00;
            r[1] = beta*r[1] + alpha*v01;
            r[stride+0] = beta*r[stride+0] + alpha*v10;
            r[stride+1] = beta*r[stride+1] + alpha*v11;
        }
        return;
    }
    if( store_mode==1 )
    {
        if( beta==0 )
        {
            r[0] = alpha*v00;
            r[1] = alpha*v01;
        }
        else
        {
            r[0] = beta*r[0] + alpha*v00;
            r[1] = beta*r[1] + alpha*v01;
        }
        return;
    }
    if( store_mode==2 )
    {
        if( beta==0 )
        {
            r[0] =alpha*v00;
            r[stride+0] = alpha*v10;
        }
        else
        {
            r[0] = beta*r[0] + alpha*v00; 
            r[stride+0] = beta*r[stride+0] + alpha*v10;
        }
        return;
    }
    if( store_mode==3 )
    {
        if( beta==0 )
        {
            r[0] = alpha*v00;
        }
        else
        {
            r[0] = beta*r[0] + alpha*v00;
        }
        return;
    }
}


/********************************************************************
This function calculates R := alpha*A'*B+beta*R where A and B are Kx2 
matrices stored in contiguous row-by-row storage,  R  is  2x2  matrix
stored in non-contiguous row-by-row storage.

A and B must be aligned; R may be non-aligned.

If beta is zero, contents of R is ignored (not  multiplied  by zero -
just ignored).

However, when alpha is zero, we still calculate A'*B, which is 
multiplied by zero afterwards.

Function accepts additional parameter store_mode:
* if 0, full R is stored
* if 1, only first row of R is stored
* if 2, only first column of R is stored
* if 3, only top left element of R is stored

This function supports SSE2; it can be used when:
1. AE_HAS_SSE2_INTRINSICS was defined (checked at compile-time)
2. ae_cpuid() result contains CPU_SSE2 (checked at run-time)

If (1) is failed, this function will still be defined and callable, but it 
will do nothing.  If (2)  is  failed , call to this function will probably 
crash your system. 

If  you  want  to  know  whether  it  is safe to call it, you should check 
results  of  ae_cpuid(). If CPU_SSE2 bit is set, this function is callable 
and will do its work.
********************************************************************/
#if defined(AE_HAS_SSE2_INTRINSICS)
void _ialglib_mm22_sse2(double alpha, const double *a, const double *b, ae_int_t k, double beta, double *r, ae_int_t stride, ae_int_t store_mode)
{
    /*
     * We calculate product of two Kx2 matrices (result is 2x2). 
     * VA and VB store result as follows:
     *
     *        [ VD[0]  VE[0] ]
     * A'*B = [              ]
     *        [ VE[1]  VD[1] ]
     *
     */
    __m128d va, vb, vd, ve, vt, vt0, vt1, r0, r1, valpha, vbeta; 
    ae_int_t t, k2, k3;
    
    /*
     * calculate product
     */
    k2 = k/2;
    vd = _mm_setzero_pd();
    ve = _mm_setzero_pd();
    for(t=0; t<k2; t++)
    {
        vb = _mm_load_pd(b);
        va = _mm_load_pd(a);
        vt = vb;
        vb = _mm_mul_pd(va,vb);
        vt = _mm_shuffle_pd(vt, vt, 1);
        vd = _mm_add_pd(vb,vd);        
        vt = _mm_mul_pd(va,vt);
        vb = _mm_load_pd(b+2);
        ve = _mm_add_pd(vt,ve);
        va = _mm_load_pd(a+2);
        vt = vb;
        vb = _mm_mul_pd(va,vb);
        vt = _mm_shuffle_pd(vt, vt, 1);
        vd = _mm_add_pd(vb,vd);
        vt = _mm_mul_pd(va,vt);
        ve = _mm_add_pd(vt,ve);
        a+=4;
        b+=4;
    }
    if( k%2 )
    {
        va = _mm_load_pd(a);
        vb = _mm_load_pd(b);
        vt = _mm_shuffle_pd(vb, vb, 1);
        vd = _mm_add_pd(_mm_mul_pd(va,vb),vd);
        ve = _mm_add_pd(_mm_mul_pd(va,vt),ve);
    }    
    
    /*
     * r0 is first row of alpha*A'*B, r1 is second row
     */
    valpha = _mm_load1_pd(&alpha);
    r0 = _mm_mul_pd(_mm_unpacklo_pd(vd,ve),valpha);
    r1 = _mm_mul_pd(_mm_unpackhi_pd(ve,vd),valpha);
    
    /*
     * store
     */
    if( store_mode==0 )
    {
        if( beta==0 )
        {
            _mm_storeu_pd(r,r0);
            _mm_storeu_pd(r+stride,r1);
        }
        else
        {
            vbeta = _mm_load1_pd(&beta);
            _mm_storeu_pd(r,_mm_add_pd(_mm_mul_pd(_mm_loadu_pd(r),vbeta),r0));
            _mm_storeu_pd(r+stride,_mm_add_pd(_mm_mul_pd(_mm_loadu_pd(r+stride),vbeta),r1));
        }
        return;
    }
    if( store_mode==1 )
    {
        if( beta==0 )
            _mm_storeu_pd(r,r0);
        else
            _mm_storeu_pd(r,_mm_add_pd(_mm_mul_pd(_mm_loadu_pd(r),_mm_load1_pd(&beta)),r0));
        return;
    }
    if( store_mode==2 )
    {
        double buf[4];
        _mm_storeu_pd(buf,r0);
        _mm_storeu_pd(buf+2,r1);
        if( beta==0 )
        {
            r[0] =buf[0];
            r[stride+0] = buf[2];
        }
        else
        {
            r[0] = beta*r[0] + buf[0]; 
            r[stride+0] = beta*r[stride+0] + buf[2];
        }
        return;
    }
    if( store_mode==3 )
    {
        double buf[2];
        _mm_storeu_pd(buf,r0);
        if( beta==0 )
            r[0] = buf[0];
        else
            r[0] = beta*r[0] + buf[0];
        return;
    }
}
#endif


/*************************************************************************
This function calculates R := alpha*A'*(B0|B1)+beta*R where A, B0  and  B1 
are Kx2 matrices stored in contiguous row-by-row storage, R is 2x4  matrix 
stored in non-contiguous row-by-row storage.

A, B0 and B1 must be aligned; R may be non-aligned.

Note  that  B0  and  B1  are  two  separate  matrices  stored in different 
locations.

If beta is zero, contents of R is ignored (not  multiplied  by zero - just 
ignored).

However,  when  alpha  is  zero , we still calculate MM product,  which is 
multiplied by zero afterwards.

Unlike mm22 functions, this function does NOT support partial  output of R 
- we always store full 2x4 matrix.
*************************************************************************/
void _ialglib_mm22x2(double alpha, const double *a, const double *b0, const double *b1, ae_int_t k, double beta, double *r, ae_int_t stride)
{
    _ialglib_mm22(alpha, a, b0, k, beta, r, stride, 0);
    _ialglib_mm22(alpha, a, b1, k, beta, r+2, stride, 0);
}

/*************************************************************************
This function calculates R := alpha*A'*(B0|B1)+beta*R where A, B0  and  B1 
are Kx2 matrices stored in contiguous row-by-row storage, R is 2x4  matrix 
stored in non-contiguous row-by-row storage.

A, B0 and B1 must be aligned; R may be non-aligned.

Note  that  B0  and  B1  are  two  separate  matrices  stored in different 
locations.

If beta is zero, contents of R is ignored (not  multiplied  by zero - just 
ignored).

However,  when  alpha  is  zero , we still calculate MM product,  which is 
multiplied by zero afterwards.

Unlike mm22 functions, this function does NOT support partial  output of R 
- we always store full 2x4 matrix.

This function supports SSE2; it can be used when:
1. AE_HAS_SSE2_INTRINSICS was defined (checked at compile-time)
2. ae_cpuid() result contains CPU_SSE2 (checked at run-time)

If (1) is failed, this function will still be defined and callable, but it 
will do nothing.  If (2)  is  failed , call to this function will probably 
crash your system. 

If  you  want  to  know  whether  it  is safe to call it, you should check 
results  of  ae_cpuid(). If CPU_SSE2 bit is set, this function is callable 
and will do its work.
*************************************************************************/
#if defined(AE_HAS_SSE2_INTRINSICS)
void _ialglib_mm22x2_sse2(double alpha, const double *a, const double *b0, const double *b1, ae_int_t k, double beta, double *r, ae_int_t stride)
{
    /*
     * We calculate product of two Kx2 matrices (result is 2x2). 
     * V0, V1, V2, V3 store result as follows:
     *
     *     [ V0[0]  V1[1] V2[0]  V3[1] ]
     * R = [                           ]
     *     [ V1[0]  V0[1] V3[0]  V2[1] ]
     *
     * VA0 stores current 1x2 block of A, VA1 stores shuffle of VA0,
     * VB0 and VB1 are used to store two copies of 1x2 block of B0 or B1
     * (both vars store same data - either B0 or B1). Results from multiplication
     * by VA0/VA1 are stored in VB0/VB1 too.
     * 
     */
    __m128d v0, v1, v2, v3, va0, va1, vb0, vb1; 
    __m128d r00, r01, r10, r11, valpha, vbeta; 
    ae_int_t t, k2;
    
    k2 = k/2;
    v0 = _mm_setzero_pd();
    v1 = _mm_setzero_pd();
    v2 = _mm_setzero_pd();
    v3 = _mm_setzero_pd();
    for(t=0; t<k; t++)
    {
        va0 = _mm_load_pd(a);
        vb0 = _mm_load_pd(b0);
        va1 = _mm_load_pd(a);
        
        vb0 = _mm_mul_pd(va0,vb0);
        vb1 = _mm_load_pd(b0);
        v0 = _mm_add_pd(v0,vb0);        
        vb1 = _mm_mul_pd(va1,vb1);
        vb0 = _mm_load_pd(b1);
        v1 = _mm_add_pd(v1,vb1);        
        
        vb0 = _mm_mul_pd(va0,vb0);
        vb1 = _mm_load_pd(b1);
        v2 = _mm_add_pd(v2,vb0);        
        vb1 = _mm_mul_pd(va1,vb1);
        v3 = _mm_add_pd(v3,vb1);        

        a+=2;
        b0+=2;
        b1+=2;
    }

    /*
     * shuffle V1 and V3 (conversion to more convenient storage format):
     *
     *     [ V0[0]  V1[0] V2[0]  V3[0] ]
     * R = [                           ]
     *     [ V1[1]  V0[1] V3[1]  V2[1] ]
     *
     * unpack results to
     *
     * [ r00 r01 ]
     * [ r10 r11 ]
     *
     */
    valpha = _mm_load1_pd(&alpha);
    v1 = _mm_shuffle_pd(v1, v1, 1);
    v3 = _mm_shuffle_pd(v3, v3, 1);
    r00 = _mm_mul_pd(_mm_unpacklo_pd(v0,v1),valpha);
    r10 = _mm_mul_pd(_mm_unpackhi_pd(v1,v0),valpha);
    r01 = _mm_mul_pd(_mm_unpacklo_pd(v2,v3),valpha);
    r11 = _mm_mul_pd(_mm_unpackhi_pd(v3,v2),valpha);
    
    /*
     * store
     */
    if( beta==0 )
    {
        _mm_storeu_pd(r,r00);
        _mm_storeu_pd(r+2,r01);
        _mm_storeu_pd(r+stride,r10);
        _mm_storeu_pd(r+stride+2,r11);
    }
    else
    {
        vbeta = _mm_load1_pd(&beta);
        _mm_storeu_pd(r,          _mm_add_pd(_mm_mul_pd(_mm_loadu_pd(r),vbeta),r00));
        _mm_storeu_pd(r+2,        _mm_add_pd(_mm_mul_pd(_mm_loadu_pd(r+2),vbeta),r01));
        _mm_storeu_pd(r+stride,   _mm_add_pd(_mm_mul_pd(_mm_loadu_pd(r+stride),vbeta),r10));
        _mm_storeu_pd(r+stride+2, _mm_add_pd(_mm_mul_pd(_mm_loadu_pd(r+stride+2),vbeta),r11));
    }    
}
#endif

}


/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS PARALLEL SUBROUTINES
//
/////////////////////////////////////////////////////////////////////////
namespace alglib_impl
{


}